Let f (v, e, Ξ») denote the maximum number of proper vertex colorings of a graph with v vertices and e edges in Ξ» colors. In this paper we present some new upper bounds for f (v, e, Ξ»). In particular, a new notion of pseudoproper colorings of a graph is given, which allows us to significantly improve
β¦ LIBER β¦
Some Algebraic Methods for Calculating the Number of Colorings of a Graph
β Scribed by Yu. V. Matiyasevich
- Book ID
- 111595618
- Publisher
- Springer US
- Year
- 2004
- Tongue
- English
- Weight
- 150 KB
- Volume
- 121
- Category
- Article
- ISSN
- 1573-8795
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## Abstract Let π» denote the family of simple undirected graphs on __v__ vertices having __e__ edges ((__v__, __e__)βgraphs) and __P__(__G__; Ξ») be the chromatic polynomial of a graph __G.__ For the given integers __v__, __e__, and Ξ», let __f__(__v__, __e__, Ξ») denote the greatest number of proper