## 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 χ^__c__^. Let Δ^\*^ be the maximum face degree of a graph. There exist
Three new upper bounds on the chromatic number
✍ Scribed by María Soto; André Rossi; Marc Sevaux
- Book ID
- 113564665
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 238 KB
- Volume
- 159
- Category
- Article
- ISSN
- 0166-218X
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A harmonious coloring of a simple graph G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We obtain a new upper bound for the harmonious chromatic number of general
The entire chromatic number χ ve f (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. conjectured that χ ve f (G) ≤ + 4 for every plane graph G. In this paper we prove the conj