منابع مشابه
On minimally b-imperfect graphs
A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number of a graph G is the largest integer k such that G admits a b-coloring with k colors. A graph is b-perfect if the b-chromatic number is equal to the chromatic number for every induced subgraph H of G. A graph is minimally b-impe...
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We prove that a minimal imperfect graph containing a vertex which is not on any P 5 has no odd pair. A graph is perfect if the vertices of any induced subgraph H can be colored, in such a way that no two adjacent vertices receive the same color, with a number of colors (denoted by (H)) not exceeding the cardinality !(H) of a maximum clique of H. A graph is minimal imperfect if all its proper in...
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Let G be a simple connected graph on 2n vertices with a perfect matching. G is k-extendable if for any set M of k independent edges, there exists a perfect matching in G containing all the edges of M. G is minimally k-extendable if G is k-extendable but G-uv is not k-extendable for every pair of adjacent vertices u and v of G. The problem that arises is that of characterizing k-extendable and m...
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The characterization of strongly perfect graphs by a restricted list of forbidden induced subgraphs has remained an open question for a long time. The minimal strongly imperfect graphs which are simultaneous imperfect are only odd holes and odd antiholes ( E. Olaru, [9]), but the entire list is not known, in spite of a lot of particular results in this direction. In this paper we give some new ...
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Let an integer s ≥ 1 and a graph G be given. Let us denote by χs(G) the smallest integer χ for which there exists a vertex-colouring of G with χ colours such that any two distinct vertices of the same colour are at a distance greater than s. Let us denote by ωs(G) the maximal cardinality of a subset of the vertices of G with diameter at most s. Clearly χs(G) ≥ ωs(G). For s ≥ 1 and h ≥ 0 set γs(...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.02.023