Results 11 to 20 of about 43,364 (297)
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 $G$, $α(H) + ω(H) \geq |V(H)|$. (Here $α$ and $ω$ denote the stability number and clique number, respectively.) We give a set of $27$ graphs and we prove that a graph $G$ is sum-perfect if and only if $G ...
Bart Litjens +2 more
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Critical perfect graphs and perfect 3-chromatic graphs
Journal of Combinatorial Theory, Series B, 1977 AbstractThis 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. Then we prove that Berge's Strong Perfect Graph Conjecture is valid for 3-chromatic graphs.
Tucker, Alan
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Random Structures & Algorithms, 2018 We investigate the asymptotic structure of a random perfect graph Pn sampled uniformly from the set of perfect graphs on vertex set . Our approach is based on the result of Prömel and Steger that almost all perfect graphs are generalised split graphs, together with a method to generate such graphs almost uniformly.
McDiarmid, C, Yolov, N
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Discrete Mathematics, 1978 AbstractAn 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 Buneman [3]), and we relate them to some well-known classes of perfect graphs.
Golumbic, Martin Charles
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Discrete Mathematics, 1977 AbstractIn this paper perfectness of various products of graphs is considered. The Cartesian product G1 × G2 is perfect iff it has no induced C2n+1 (n ⩾ 2). By considering the various sufficient conditions for the latter condition, perfect Cartesian products are characterized. Similarly perfect tensor products G1 × G2 are characterized and it is proved
G. Ravindra, K. R. Parthasarathy
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Decomposition of perfect graphs
Journal of Combinatorial Theory, Series B, 1987 In this paper we describe general composition and decomposition schemes for perfect graphs, which covers almost all recent results in this area, e.g. the amalgam and the 2-amalgam split. Our approach is based on the consideration of induced cycles and their complements in perfect graphs (as opposed to the consideration of cycles for defining ...
Wen-Lian Hsu, Hsu, Wen-Lian
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Electronic Notes in Discrete Mathematics, 1999 Two graphs \(G\) and \(H\) on the vertex set \(V\) are \(P_4\)-isomorphic if there is a permutation \(\pi\) on \(V\) such that, for all subsets \(S\) of \(V\), \(S\) induces a chordless \(P_4\) in \(G\) if and only if \(\pi (S)\) induces a \(P_4\) in \(H\). The author characterizes all graphs \(P_4\)-isomorphic to a bipartite graph. For example, we can
Van Bang Le, Bang Le, Van
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Journal of Combinatorial Theory, Series B, 1990 A colouring of the vertices of a graph is said to be locally perfect if for each vertex x the neighbourhood N(x) of x is coloured by a number of colours which is equal to the cardinality of a maximum clique in N(x). The locally perfect graphs are those graphs for which any subgraph has a locally perfect colouring. It is shown in this paper that locally
Preissmann, Myriam, Myriam Preissmann
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Journal of Graph Theory, 2005 AbstractFor 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, …, k − 1, in which i ∼j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is
Pêcher, Arnaud +3 more
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Discrete Mathematics, 1986 Let G be a graph. The authors denote by \(\alpha_ N(G)\) the maximum number of edges of G such that no two of them belong to the same neighborhood subgraph of G (that is a subgraph induced by a vertex v and the vertices adjacent to v). They denote by \(\rho_ N(G)\) the minimum number of vertices whose neighborhood subgraphs cover the edge set of G.
Jenö Lehel, Zsolt Tuza
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