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Graph which partitions into a clique and independent set
graph theory, a branch of mathematics, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs
Split_graph
Complete bipartite cut in a graph
In graph theory, a split of an undirected graph is a cut whose cut-set forms a complete bipartite graph. A graph is prime if it has no splits. The splits
Split_(graph_theory)
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes
Glossary_of_graph_theory
Graph with tight clique-coloring relation
In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every
Perfect_graph
Distance of a graph from a split graph
In graph theory, a branch of mathematics, the splittance of an undirected graph measures its distance from a split graph. A split graph is a graph whose
Splittance
Graph formed by adding isolated or universal vertices
and a split graph. Every graph that is both a trivially perfect graph and the complementary graph of a trivially perfect graph is a threshold graph. Threshold
Threshold_graph
Graph divided into two independent sets
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets
Bipartite_graph
In the mathematical field of graph theory, a word-representable graph is a graph that can be characterized by a word (or sequence) whose entries alternate
Word-representable_graph
self-complementary graph, a block graph, a split graph, an interval graph, a claw-free graph, a 1-vertex-connected graph and a 1-edge-connected graph. A graph is bull-free
Bull_graph
Adjacent subset of an undirected graph
cover. A perfect graph is a graph in which the clique number equals the chromatic number in every induced subgraph. A split graph is a graph in which some
Clique_(graph_theory)
Topics referred to by the same term
destroyer Split, decommissioned in 1980 Yugoslav frigate Split, Koni-class Split (graph theory) Split (mathematics), a property of an exact sequence Split Lie
Split
Perfect graphs have neither odd holes nor odd antiholes
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither
Strong_perfect_graph_theorem
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
One of two types of graph
tripartite graph K1,1,p. It is a graph consisting of p {\displaystyle p} triangles sharing a common edge. A book of this type is a split graph. This graph has
Book_(graph_theory)
Partition of a graph's nodes into 2 disjoint subsets
in the tree. Connectivity (graph theory) Graph cuts in computer vision Split (graph theory) Vertex separator Bridge (graph theory) Cutwidth Dicut "NetworkX
Cut_(graph_theory)
Graph where all long cycles have a chord
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not
Chordal_graph
Intersection graph for intervals on the real number line
comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph and a permutation graph. The
Interval_graph
of graph theory, the sphericity of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as
Sphericity_(graph_theory)
Intersection graph of trapezoids between parallel lines
In graph theory, trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They are a class of co-comparability graphs that
Trapezoid_graph
Software for inferring bioinformatics split graphs
inferring phylogenetic trees, phylogenetic networks, or, more generally, split graphs, from various types of data such as a sequence alignment, a distance
SplitsTree
Graph with same nodes as but complementary connections to another
In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices are
Complement_graph
Split graph String graph Strongly regular graph Threshold graph Total graph Tree (graph theory). Trellis (graph) Turán graph Ultrahomogeneous graph Vertex-transitive
List_of_graph_theory_topics
Number of vertices with unambiguous distances
bounded-degree planar graphs, split graphs, bipartite graphs and their complements, line graphs of bipartite graphs, unit disk graphs, interval graphs of diameter
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
permutation is skew-merged if and only if its associated permutation graph is a split graph, a graph that can be partitioned into a clique (corresponding to the
Skew-merged_permutation
Unsolved problem in computational complexity theory
bipartite Eulerian graphs bipartite regular graphs line graphs split graphs chordal graphs regular self-complementary graphs polytopal graphs of general, simple
Graph_isomorphism_problem
In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has
Chordal_bipartite_graph
Topics referred to by the same term
"Books", an episode from Ben & Holly's Little Kingdom Book (graph theory), a split graph consisting of p triangles sharing a common edge Book (wagering)
Book_(disambiguation)
Maths conjecture
that the conjecture has been proven for are the Hansen polytopes of split graphs, which had been used by Ragnar Freij, Matthias Henze, and Moritz Schmitt
Kalai's_3^d_conjecture
integer k > 1, G cannot be split into k different connected components by the removal of fewer than tk vertices. For instance, a graph is 1-tough if the number
Graph_toughness
Cycles in a graph that cover each edge twice
In graph-theoretic mathematics, a cycle double cover is a collection of cycles in an undirected graph that together include each edge of the graph exactly
Cycle_double_cover
Graph with a median for each three vertices
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a {\displaystyle a} , b {\displaystyle
Median_graph
Query language for property graphs
GQL (Graph Query Language) is a standardized query language for property graphs first described in ISO/IEC 39075, released in April 2024 by ISO/IEC. The
Graph_Query_Language
cocolorings of G. The graphs with cochromatic number 2 are exactly the bipartite graphs, complements of bipartite graphs, and split graphs. As the requirement
Cocoloring
Subset of a graph's nodes such that all other nodes link to at least one
In graph theory, a dominating set for a graph G is a subset D of its vertices, such that any vertex of G is in D, or has a neighbor in D. The domination
Dominating_set
Psychoanalytic tool devised by Jacques Lacan
The graph of desire (French: graphe du désir) is a conceptual tool in Lacanianism. Lacan devised numerous quasi-mathematical diagrams to represent the
Graph_of_desire
Belarusian mathematician (1929–2019)
introduction and investigation of the class of split graphs and for her contributions to line graphs of hypergraphs. In 1998, she was awarded the Belarus
Regina_Tyshkevich
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Graphical representation of a computer program or algorithm
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a function during
Control-flow_graph
In graph theory and computer science, the graph sandwich problem is a problem of finding a graph that belongs to a particular family of graphs and is
Graph_sandwich_problem
Vowel split in English
Trap–bath split An example of the trap–bath split Problems playing this file? See media help. The TRAP–BATH split is a vowel split that occurs mainly in
Trap–bath_split
Constructs with triply-connected vertices
2-connected graphs are defined as usual. This leaves the other graphs in the 3-connected class because each 3-regular graph can be split by cutting all
Table_of_simple_cubic_graphs
Flow graph invented by Claude Shannon
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the
Signal-flow_graph
Graph in which all ordered pairs of linked nodes are automorphic
In the mathematical field of graph theory, a graph G is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices ( u 1 , v 1 )
Symmetric_graph
Representation of a graph's triconnected components
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex
SPQR_tree
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Computer compiler optimization technique
register allocation), or across function boundaries traversed via call-graph (interprocedural register allocation). When done per function/procedure
Register_allocation
Graph coloring with equal color classes
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No
Equitable_coloring
Chordal graph where all cycles of even length have odd chords
In the mathematical area of graph theory, an undirected graph G is strongly chordal if it is a chordal graph and every cycle of even length (≥ 6) in G
Strongly_chordal_graph
Graph formed by complementation and disjoint union
In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation
Cograph
Embedding a graph in a topological space, often Euclidean
In topological graph theory, an embedding (also spelled imbedding) of a graph G {\displaystyle G} on a surface Σ {\displaystyle \Sigma } is a representation
Graph_embedding
Graphs whose distances obey Ptolemy's inequality
In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek
Ptolemaic_graph
Fewest cliques covering a graph's edges
In the mathematical field of graph theory, the intersection number of a graph G = ( V , E ) {\displaystyle G=(V,E)} is the smallest number of elements
Intersection number (graph theory)
Intersection_number_(graph_theory)
Graph whose induced subgraphs preserve distance
In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances
Distance-hereditary_graph
Technique for drawing non-planar graphs
mathematical field of graph theory, planarization is a method of extending graph drawing methods from planar graphs to graphs that are not planar, by
Planarization
Measure of the structural complexity of a software program
Cyclomatic complexity is computed using the control-flow graph of the program. The nodes of the graph correspond to indivisible groups of commands of a program
Cyclomatic_complexity
Baseball pitch
"Remembering Roger Craig, Sage of the Split-Fingered Fastball (1930–2023)". FanGraphs. Retrieved May 24, 2025. "Who Invented the Split Finger Fastball: A Journey
Split-finger_fastball
Measure of whether or not a graph has a "bottleneck"
(also Cheeger number or isoperimetric number) of a graph is a numerical measure of whether or not a graph has a "bottleneck". The Cheeger constant as a measure
Cheeger constant (graph theory)
Cheeger_constant_(graph_theory)
Problem of finding the longest simple path for a given graph
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A
Longest_path_problem
Graph where any two induced paths between nodes both have odd or even lengths
In graph theory, a parity graph is a graph in which all induced paths between the same two vertices have the same parity: either all paths have odd length
Parity_graph
In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels
Radio_coloring
Mathematical measure for partial orders
(planar graph with fixed plane embedding) is at most four. Felsner later proved in "The order dimension of planar maps revisited " that dim ( split ( P M
Order_dimension
Decision support tool
using the phi function to split the nodes and one decision tree will be built using the information gain function to split the nodes. The main advantages
Decision_tree
Deleting a graph edge and merging its nodes
In graph theory, an edge contraction is an operation that removes an edge from a graph while simultaneously merging the two vertices that it previously
Edge_contraction
Postclassic dated to 1530, but Spanish Period dated 1544 – 1700, and further split into two unnamed sub-periods dated 1544–1641 and 1641–1700, respectively
Periodisation of the history of Belize
Periodisation_of_the_history_of_Belize
Statement in mathematical combinatorics
its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. As
Ramsey's_theorem
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
noncommutative signal-flow graph is a tool for modeling interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring
Noncommutative signal-flow graph
Noncommutative_signal-flow_graph
Cooling of air in an enclosed space
temperature and relative temperature between sink and system, and is often graphed or averaged against expected conditions. Air conditioner equipment power
Air_conditioning
In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs G and H is a graph that is an induced subgraph of both
Maximum common induced subgraph
Maximum_common_induced_subgraph
Partition of a simple polygon into triangles
cases of planar straight-line graphs. When there are no holes or added points, triangulations form maximal outerplanar graphs. Over time, a number of algorithms
Polygon_triangulation
Every graph has evenly many odd vertices
In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges
Handshaking_lemma
Dominating set that dominates both a graph and its complement
problem remains NP-hard even for restricted graph classes, including planar graphs and split graphs. For split graphs, any global dominating set is formed either
Global_dominating_set
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
In computer science, an interval union-split-find data structure is a data structure that stores a partition of the integer interval [ 1 , n ] {\displaystyle
Interval_union-split-find
Models signal dispersion by representing the radio propagation environment by a graph
Propagation graphs are a mathematical modelling method for radio propagation channels. A propagation graph is a signal flow graph in which vertices represent
Propagation_graph
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split into
Planar_separator_theorem
Assignment of colors to edges of a graph
In graph theory, a proper edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color
Edge_coloring
Algorithm for two disjoint paths in a graph
algorithm for finding two disjoint paths in a nonnegatively-weighted directed graph, so that both paths connect the same pair of vertices and have minimum total
Suurballe's_algorithm
Characterization of graphs with perfect matchings
mathematical discipline of graph theory, the Tutte theorem, named after William Thomas Tutte, is a characterization of finite undirected graphs with perfect matchings
Tutte's theorem on perfect matchings
Tutte's_theorem_on_perfect_matchings
Operation in graph theory
In graph theory, local complementation (also known as vertex inversion) is an operation on a graph that toggles adjacencies among the neighbours of a
Local_complementation
Clustering and community detection algorithm
split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each
Leiden_algorithm
Open-source data analytics cluster computing framework
Malak, Michael (14 June 2016). "Finding Graph Isomorphisms In GraphX And GraphFrames: Graph Processing vs. Graph Database". slideshare.net. sparksummit
Apache_Spark
Family of graphs based on the Fibonacci sequence
In the mathematical field of graph theory, the Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties
Fibonacci_cube
2026 Android mobile operating system
2026. Retrieved March 11, 2026. Abner Li (January 13, 2026). "Android 17' split Notifications & Quick Settings panels leak in full [Gallery]". 9To5Google
Android_17
Clustering and community detection algorithm
function aggregateGraph returns a new graph whose vertices are the partition of the old graph, and whose edges are calculated using the old graph. This function
Louvain_method
Process of generalization
they are not abstract in the sense of the objects in graph 1 below. We might look at other graphs, in a progression from cat to mammal to animal, and see
Abstraction
combinatorist Regina Tyshkevich (1929–2019), Belarusian graph theorist, co-invented split graphs Galina Tyurina (1938–1970), Soviet algebraic geometer Olabisi
List_of_women_in_mathematics
Graphical technique for data sets
plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be
Plot_(graphics)
Academic journal
and applications of combinatorics. Series B is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the
Journal of Combinatorial Theory
Journal_of_Combinatorial_Theory
Partition refinement forms a key component of several efficient algorithms on graphs and finite automata, including DFA minimization, the Coffman–Graham algorithm
Partition_refinement
Theorem in graph theory
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number
Menger's_theorem
be split. In some cases, the independent tiles' results can be fused to approximate the true results. An alternative exists in the form of graph-based
Minimum spanning tree-based segmentation
Minimum_spanning_tree-based_segmentation
Highly connected subgraph
The problem remains NP-hard in bipartite graphs and chordal graphs but is polynomial for trees and split graphs. It is open whether the problem is NP-hard
Dense_subgraph
Bipartition of a set of taxa
A split in phylogenetics is a bipartition of a set of taxa, and the smallest unit of information in unrooted phylogenetic trees: each edge of an unrooted
Split_(phylogenetics)
Four-dimensional number system
Charles F.F. (January 2007). "Quaternions in molecular modeling". J. Mol. Graph. Mod. 25 (5): 595–604. arXiv:physics/0506177. Bibcode:2007JMGM...25..595K
Quaternion
Pandemic caused by SARS-CoV-2
such as ear savers, non-invasive ventilation helmets, and ventilator splitters. In July 2021, several experts expressed concern that achieving herd immunity
COVID-19_pandemic
Phenomenon, particularly on IRC, in which one server becomes disconnected from others
disconnection between two servers. A split between any two servers splits the entire network into two pieces. Consider the graph to the right, which represents
Netsplit
Genomic analysis technique
topologically associating domains with ultra-low resolution Hi-C data by graph structural entropy". Nature Communications. 9 (1): 3265. Bibcode:2018NatCo
Hi-C (genomic analysis technique)
Hi-C_(genomic_analysis_technique)
Partition of the vertices of a graph
In graph theory, the Gallai–Edmonds decomposition is a partition of the vertices of a graph into three subsets which provides information on the structure
Gallai–Edmonds_decomposition
Path-finding using high-weight graph edges
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight
Widest_path_problem
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