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Adjacent strong edge colorings and total colorings of regular graphs

✍ Scribed by ZhongFu Zhang; Douglas R. Woodall; Bing Yao; JingWen Li; XiangEn Chen; Liang Bian


Book ID
107347882
Publisher
SP Science China Press
Year
2009
Tongue
English
Weight
201 KB
Volume
52
Category
Article
ISSN
1674-7283

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πŸ“œ SIMILAR VOLUMES


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Let x'(G), called the strong coloring number of G, denote the minimum number of colors for which there is a proper edge coloring of a graph G in which no two of its vertices is incident to edges colored with the same set of colors. It is shown that Z'~(G) ~< Fcn], Β½ < c ~ 1, whenever A(G) is appropr

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Adjacent strong edge coloring of graphs
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For a graph G(V, E), if a proper k-edge coloring f is satisfied with C(u) # C(V) for UZ) E E(G), where C(u) = {f(~v) 1 UZI E E}, then f is called k-adjacent strong edge coloring of G. is abbreviated k-ASEC, and xbs(G) = min{k 1 k-ASEC of G} is called the adjacent strong edge chromatic number of G. I

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We define the incidence coloring number of a graph and bound it in terms of the maximum degree. The incidence coloring number turns out to be the strong chromatic index of an associated bipartite graph. We improve a bound for the strong chromatic index of bipartite graphs all of whose cycle lengths

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✍ Darryn Bryant; Barbara Maenhaut πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 127 KB

## Abstract For __k__ = 1 and __k__ = 2, we prove that the obvious necessary numerical conditions for packing __t__ pairwise edge‐disjoint __k__‐regular subgraphs of specified orders __m__~1~,__m__~2~,… ,__m__~t~ in the complete graph of order __n__ are also sufficient. To do so, we present an edge