In this paper, we prove that any graph G with maximum degree รG ! 11 p 49ร241AEa2, which is embeddable in a surface AE of characteristic 1AE 1 and satisยฎes jVGj b 2รGร5ร2 p 6รG, is class one.
Edge Colorings of Embedded Graphs
โ Scribed by Zhongde Yan; Yue Zhao
- Publisher
- Springer Japan
- Year
- 2000
- Tongue
- English
- Weight
- 125 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
We characterize those graphs which have at least one embedding into some surface such that the faces can be properly colored in four or fewer colors. Embeddings into both orientable and nonorientable surfaces are considered.
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2โcolored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __aโฒ__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __aโฒ__(_
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], ยฝ < c ~ 1, whenever A(G) is appropr
An edge-coloring of a graph G is equitable if, for each v โ V (G), the number of edges colored with any one color incident with v differs from the number of edges colored with any other color incident with v by at most one. A new sufficient condition for equitable edge-colorings of simple graphs is