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Critical perfect graphs and perfect 3-chromatic graphs [PDF]
Journal of Combinatorial Theory, Series B, 1977 This paper builds on results based on D. R. Fulkerson's antiblocking polyhedra approach to perfect graphs to obtain information about critical perfect graphs and related clique-generated graphs.
Tucker, Alan
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Discussiones Mathematicae Graph Theory, 2013 Given a graph G = (V,E) and a set Lv of admissible colors for each vertex v ∈ V (termed the list at v), a list coloring of G is a (proper) vertex coloring ϕ : V → S v2V Lv such that ϕ(v) ∈ Lv for all v ∈ V and ϕ(u) 6= ϕ(v) for all uv ∈ E.
Tuza Zsolt
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Discrete Applied Mathematics, 2019 Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set
Vaidy Sivaraman +8 more
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Decomposition of perfect graphs [PDF]
Journal of Combinatorial Theory, Series B, 1987 We describe composition and decomposition schemes for perfect graphs, which generalize all recent results in this area, e.g., the amalgam and the 2-amalgam split.
Wen-Lian Hsu, Hsu, Wen-Lian
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Journal of Combinatorial Theory, Series B, 1990 A new property of minimal imperfect graphs is given. This leads to a way to add a new vertex to a perfect graph so that the resulting graph remains perfect. It is shown that the same holds for strongly perfect graphs.
Preissmann, Myriam, Myriam Preissmann
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Neighborhood perfect graphs [PDF]
Discrete Mathematics, 1986 The notion of neighborhood perfect graphs is introduced here as follows. Let G be a graph, αN(G) denote the maximum number of edges such that no two of them belong to the same subgraph of G induced by the (closed) neighborhood of some vertex; let ϱN(G ...
Tuza, Zs, Lehel, J
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Trivially perfect graphs [PDF]
Discrete Mathematics, 1978 An undirected graph is trivially perfect if for every induced subgraph the stability number equals the number of (maximal) cliques. We characterize the trivially perfect graphs as a proper subclass of the triangulated graphs (thus disproving a claim of ...
Golumbic, Martin Charles
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Electronic Journal of Graph Theory and ApplicationsA perfect dominating set in a graph G = (V, E) is a subset S ⊆ V such that each vertex in V \ S has exactly one neighbor in S. A perfect coalition in G consists of two disjoint sets of vertices V1 and V2 such that i) neither V1 nor V2 is a dominating set,
Doost Ali Mojdeh +1 more
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On clique-perfect and K-perfect graphs
Ars Comb., 2006 A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H is equal to the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G.
Guillermo Durán +3 more
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Perfect Nilpotent Graphs [PDF]
Kragujevac Journal of Mathematics, 2021 Let R be a commutative ring with identity. The nilpotent graph of R, denoted by ΓN(R), is a graph with vertex set ZN(R)∗, and two vertices x and y are adjacent if and only if xy is nilpotent, where ZN(R) = {x ∈ R∣xy is nilpotent, for some y ∈ R∗}. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the ...
Nikmehr, M. J., Azadi, A.
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