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Journal of Graph Theory, 1999
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Information Processing Letters, 1994
The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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Graphs and Combinatorics, 1991
Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986.
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Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986.
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J. Comb. Theory B, 1996
Let \(\delta(G)\) and \(\chi(G)\) denote the minimum degree and chromatic number of the simple graph \(G\) respectively. Define \(\beta(G)=1+\max\{\delta(H)\}\) where \(H\) varies over all the induced subgraphs of \(G\). It is clear that \(\beta(G)\leq \chi(G)\) and \(G\) is said to be \(\beta\)-perfect if \(\beta(H)= \chi(H)\) for each induced ...
S. E. Markossian +2 more
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Let \(\delta(G)\) and \(\chi(G)\) denote the minimum degree and chromatic number of the simple graph \(G\) respectively. Define \(\beta(G)=1+\max\{\delta(H)\}\) where \(H\) varies over all the induced subgraphs of \(G\). It is clear that \(\beta(G)\leq \chi(G)\) and \(G\) is said to be \(\beta\)-perfect if \(\beta(H)= \chi(H)\) for each induced ...
S. E. Markossian +2 more
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SIAM Journal on Algebraic Discrete Methods, 1982
Let P be a simply connected polyomino. Let $G( P )$ be the graph whose vertices are the maximal rectangles in P, two such vertices being adjacent if the corresponding rectangles have nontrivial intersection. In this paper we show that $G ( P )$ is perfect. This solves a problem posed by Berge et al.
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Let P be a simply connected polyomino. Let $G( P )$ be the graph whose vertices are the maximal rectangles in P, two such vertices being adjacent if the corresponding rectangles have nontrivial intersection. In this paper we show that $G ( P )$ is perfect. This solves a problem posed by Berge et al.
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Mathematical Methods of Operations Research, 2008
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Mathematical Programming, 1991
The author introduces four types of norms on \(R^ n\) derived on the basis of the family of all maximal cliques of an \(n\)-vertex graph (or its complement) and related to the fractional vertex packing polytope of the graph. The goal of the paper is to demonstrate the usefulness of employing techniques of functional analysis to obtain results in graph ...
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The author introduces four types of norms on \(R^ n\) derived on the basis of the family of all maximal cliques of an \(n\)-vertex graph (or its complement) and related to the fractional vertex packing polytope of the graph. The goal of the paper is to demonstrate the usefulness of employing techniques of functional analysis to obtain results in graph ...
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Mathematical Programming, 1977
The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3.
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The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3.
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Sci. Ann. Cuza Univ., 1993
The aim of this paper is to introduce a new class of perfect graphs, \(C\)-perfect graphs, which strictly contains perfectly orderable graphs and Meyniel graphs and is contained in the class of strongly perfect graphs.
Cornelius Croitoru, Costel Radu
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The aim of this paper is to introduce a new class of perfect graphs, \(C\)-perfect graphs, which strictly contains perfectly orderable graphs and Meyniel graphs and is contained in the class of strongly perfect graphs.
Cornelius Croitoru, Costel Radu
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Journal of Graph Theory, 1999
A graph \(G\) is \text{perfect} if, for each induced subgraph \(G'\) of \(G\), the chromatic number of \(G'\) equals the maximum number of pairwise adjacent vertices in \(G'\). A graph \(G\) is \text{critically perfect} if \(G\) is perfect, has no isolated vertices, and, for each edge \(e\) of \(G\), \(G - e\) is not perfect.
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A graph \(G\) is \text{perfect} if, for each induced subgraph \(G'\) of \(G\), the chromatic number of \(G'\) equals the maximum number of pairwise adjacent vertices in \(G'\). A graph \(G\) is \text{critically perfect} if \(G\) is perfect, has no isolated vertices, and, for each edge \(e\) of \(G\), \(G - e\) is not perfect.
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