منابع مشابه
A Bound on the Total Chromatic Number
We prove that the total chromatic number of any graph with max imum degree is at most plus an absolute constant In particular we show that for su ciently large the total chromatic number of such a graph is at most The proof is probabilistic
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The total chromatic number, Z"(G), of a graph G, is defined to be the minimum number ofcolours needed to colour the vertices and edges of a graph in such a way that no adjacent vertices, no adjacent edges and no incident vertex and edge are given the same colour. This paper shows that )('(G) _< z'(G) + 2x/~G), where z(G)is the vertex chromatic number and )((G)is the edge chromatic number of the...
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In this work we give a new lower bound on the chromatic number of a Mycielski graph Mi. The result exploits a mapping between the coloring problem and a multiprocessor task scheduling problem. The tightness of the bound is proved for i = 1; : : : ; 8. c © 2001 Elsevier Science B.V. All rights reserved.
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A cyclic coloring of a plane graph is a vertex coloring such that vertices incident with the same face have distinct colors. The minimum number of colors in a cyclic coloring of a graph is its cyclic chromatic number χc . Let ∗ be themaximum face degree of a graph. There exist plane graphs with χc = 2 ∗ . Ore and Plummer [5] proved that χc ≤ 2 ∗, which bound was improved to 5 ∗ by Borodin, Sand...
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ژورنال
عنوان ژورنال: COMBINATORICA
سال: 1998
ISSN: 0209-9683
DOI: 10.1007/pl00009820