A graph is (rn, k)-colorable if its vertices can be colored with rn colors in such a way that each vertex is adjacent to at most k vertices of the same color as itself. In a recent paper Cowen. Cowen, and Woodall proved that, for each compact surface S, there exists an integer k = k(S) such that eve
โฆ LIBER โฆ
Defective colorings of graphs in surfaces: Partitions into subgraphs of bounded valency
โ Scribed by L. J. Cowen; R. H. Cowen; D. R. Woodall
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 388 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
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If G is a graph on n vertices and r 2 2, w e let m,(G) denote the minimum number of complete multipartite subgraphs, with r or fewer parts, needed to partition the edge set, f(G). In determining m,(G), w e may assume that no two vertices of G have the same neighbor set. For such reduced graphs G, w