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== Bull-free graphs == ...or2-link=Najiba Sbihi|title=Recognizing bull-free perfect graphs|journal=[[Graphs and Combinatorics]]|volume=11|year=1995|pages=171–178|issue=2|doi=10.1007/B ...

| contribution = Which graphs have integral spectra? | title = Graphs and Combinatorics: Proceedings of the Capital Conference on Graph Theory an ...

...An <math>O(VE)</math> algorithm for ear decompositions of matching-covered graphs|journal=ACM Transactions on Algorithms|volume=1|issue=2|pages=324–337|doi=1 == Algorithms for general graphs == ...

...rk (with his student G. Ravindra) proving the special case of the [[strong perfect graph conjecture]] for [[claw-free graph]]s.<ref>{{citation ...The strong perfect-graph conjecture is true for <math>K_{1,3}</math>-free graphs ...

..." because they have an even number of edges, and are "central" because a [[perfect matching]] is able to be created with the remaining graph (cycle 3 leaves n ...K_{3,3}</math> does not, nor do infinitely many other minimal non-Pfaffian graphs. ...

...the order in which colors are chosen for its vertices. That is, for these graphs, the [[chromatic number]] (minimum number of colors) and [[Grundy number]] ...raphs include the [[complete graph]]s and odd-length [[cycle graph]]s (the graphs that form the exceptional cases to [[Brooks' theorem]]) as well as the [[co ...

...iltonian Graph}}</ref><br>[[Bipartite graph|Bipartite]]<br>[[Perfect graph|Perfect]]<br>[[Eulerian graph|Eulerian]]<br>[[1-walk regular graph|1-walk regular]] ...R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.</ref> ...

{{short description|Graph family made by joining complete graphs at a universal node}} ...l vertex]]. That is, it is a [[clique-sum|1-clique-sum]] of these complete graphs.<ref>{{cite journal |last=Gallian |first=J. A. | author-link = Joseph Galli ...

...av|date=2011-11-01|title=A Simpler Linear-Time Recognition of Circular-Arc Graphs|journal=Algorithmica|language=en|volume=61|issue=3|pages=694–737|doi=10.100 ...rdless cycles ''C''₅, ''C''₇, etc., are circular-arc graphs. ...

...[[longest path problem|longest paths]] and [[graph coloring|colorings]] in graphs, and to the [[Erdős–Szekeres theorem]] on monotonic subsequences. ...txt|Lovász|1972}} states that the complements of perfect graphs are always perfect, and can be used to deduce Dilworth's theorem from Mirsky's theorem and vic ...

...y an edge if and only if the corresponding trapezoids intersect. Trapezoid graphs were introduced by [[Ido Dagan|Dagan]], [[Martin Charles Golumbic|Golumbic] ...2.<ref>Ido Dagan, Martin Charles Golumbic, and Ron Yair Pinter. Trapezoid graphs and their coloring. Discrete Appl. Math., 35–46, 1988.</ref> ...

...ding of an information source having ambiguous alphabet and the entropy of graphs.|journal=6th Prague Conference on Information Theory|pages= 411–425}}</ref> ...G. Simonyi, "Perfect graphs and graph entropy. An updated survey," Perfect Graphs, John Wiley and Sons (2001) pp. 293-328, Definition 2”</ref> ...

{{Short description|Graphs whose distances obey Ptolemy's inequality}} ...s by which any distance-hereditary graph can be constructed. For Ptolemaic graphs, the neighbors of false twins are restricted to form a clique, preventing t ...

...tics|Does forbidding both a tree and a clique as induced subgraphs produce graphs of bounded chromatic number?}} ...nt number of colors. Equivalently, it asks whether the <math>T</math>-free graphs are [[χ-bounded|<math>\chi</math>-bounded]].{{r|s97}} ...

...ph|Bipartite]]<br>[[Triangle-free graph|Triangle-free]]<br>[[Perfect graph|Perfect]]<br>[[vertex-transitive graph|Vertex-transitive]] ...graph|vertex-connected]] and 3-[[k-edge-connected graph|edge-connected]] [[perfect graph]]. ...

...nversion (discrete mathematics)|reversed]] by the permutation. Permutation graphs may also be defined [[Geometric graph theory|geometrically]], as the [[inte Permutation graphs have several other equivalent characterizations: ...

...ition|sufficient conditions]] for existence of a [[Matching in hypergraphs|perfect matching in a hypergraph]], based only on the [[Degree (graph theory)|degre === Degrees and matchings in graphs === ...

...th>v</math> recovers the graph <math>G</math>, and maps the <math>k</math> perfect matchings of <math>G'</math> onto <math>k</math> 2-factors of <math>G</math ...The theorem appears first in the 1891 article ''"Die Theorie der regulären graphs"''. To prove the theorem, Petersen's fundamental idea was to 'colour' the e ...

{{Short description|Refinement of perfect matching theorems}} ...ein Ore]].<ref>{{Cite journal|last=Ore|first=Oystein|date=1955-12-01|title=Graphs and matching theorems|url=https://projecteuclid.org/euclid.dmj/1077466548|j ...

...ayley graph | Cayley graphs]], in particular, [[circulant graph |circulant graphs]], and many of their decompositions come from the action of a [[permutation ...