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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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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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Combinatorica, 1993
By a kernel of a digraph \(D\) is meant a set of vertices which is both independent and absorbant. In 1988, \textit{C. Berge} and \textit{P. Duchet} conjectured that an undirected graph \(G\) is perfect iff for an orientation \(D\) of \(G\) (where pairs of opposite arcs are allowed), if every clique of \(D\) has a kernel then \(D\) itself has a kernel.
Mostafa Blidia +2 more
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By a kernel of a digraph \(D\) is meant a set of vertices which is both independent and absorbant. In 1988, \textit{C. Berge} and \textit{P. Duchet} conjectured that an undirected graph \(G\) is perfect iff for an orientation \(D\) of \(G\) (where pairs of opposite arcs are allowed), if every clique of \(D\) has a kernel then \(D\) itself has a kernel.
Mostafa Blidia +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, 1978
Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a ...
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Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a ...
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Perfect state transfer on Cayley graphs over dihedral groups
Linear and Multilinear Algebra, 2021Xiwang Cao, Keqin Feng
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On some graph classes related to perfect graphs: A survey
Discrete Applied Mathematics, 2020Flavia Bonomo +2 more
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Perfection of glued graphs of perfect original graphs
A graph G is perfect if the chromatic number and the clique number have the same value for every of its induced subgraph. A glued graph results from combining two vertex-disjoint graphs by identifying nontrivial connected isomorphic subgraphs of both graphs. Such subgraphs are referred to as the clones.openaire +1 more source
Perfect state transfer in integral circulant graphs
Applied Mathematics Letters, 2009Milan Basic +2 more
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