## Abstract Let ${\cal F}\_{{2}{k},{k}^{2}}$ consist of all simple graphs on 2__k__ vertices and ${k}^{2}$ edges. For a simple graph __G__ and a positive integer $\lambda$, let ${P}\_{G}(\lambda)$ denote the number of proper vertex colorings of __G__ in at most $\lambda$ colors, and let $f(2k, k^{2
Algorithms for maximum k-colorings and k-coverings of transitive graphs
✍ Scribed by Fǎnicǎ Gavril
- Publisher
- John Wiley and Sons
- Year
- 1987
- Tongue
- English
- Weight
- 356 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0028-3045
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✦ Synopsis
Consider a graph G and a positive integer k. The maximum k-coloring problem is to color a maximum number of vertices using k colors, such that no two adjacent vertices have the same color. The maximum k-covering problem is to find k disjoint cliques covering a maximum number of vertices. The present paper contains polynomial time algorithms for finding maximum k-colorings and maximum k-coverings of transitive graphs.
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## Abstract In this note we show how coverings induced by voltage assignments can be used to produce packings of disjoint copies of the Hoffman‐Singleton graph into __K__~50~. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 408–412, 2003; Published online in Wiley InterScience (www.interscience
## Abstract A graph __G__ is (__k__,0)‐colorable if its vertices can be partitioned into subsets __V__~1~ and __V__~2~ such that in __G__[__V__~1~] every vertex has degree at most __k__, while __G__[__V__~2~] is edgeless. For every integer __k__⩾0, we prove that every graph with the maximum average