## Abstract A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield sho
A Note on the m-Bounded Chromatic Number of a Tree
β Scribed by Bor-Liang Chen; Ko-Wei Lih
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 77 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
β¦ Synopsis
The (m)-bounded chromatic number of a graph (G) is the smallest number of colors required for a proper coloring of (G) in which each color is used at most (m) times. We will establish an exact formula for the (m)-bounded chromatic number of a tree.
π SIMILAR VOLUMES
In 1969, Ore and Plummer defined an angular coloring as a natural extension of the Four Color Problem: a face coloring of a plane graph where faces meeting even at a vertex must have distinct colors. A natural lower bound is the maximum degree 2 of the graph. Some graphs require w 3 2 2x colors in a
## Abstract Let Ξ»(__G__) be the lineβdistinguishing chromatic number and __x__β²(__G__) the chromatic index of a graph __G__. We prove the relation Ξ»(__G__) β₯ __x__β²(__G__), conjectured by Harary and Plantholt. Β© 1993 John Wiley & Sons, Inc.
## Abstract 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 Ο^__c__^. Let Ξ^\*^ be the maximum face degree of a graph. There exist