## Abstract Given a “forbidden graph” __F__ and an integer __k__, an __F‐avoiding k‐coloring__ of a graph __G__ is a __k__‐coloring of the vertices of __G__ such that no maximal __F__‐free subgraph of __G__ is monochromatic. The __F‐avoiding chromatic number__ __ac__~__F__~(__G__) is the smallest i
COLORING SUBGRAPHS OF THE RADO GRAPH
✍ Scribed by N. W. Sauer*
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 300 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0209-9683
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📜 SIMILAR VOLUMES
A graph G is called k-critical if x(G) = k and x(G -e) -C x(G) for each edge e of G, where x denotes the chromatic number. T. Gallai conjectured that every k-critical graph of order n contains at most n complete (kl)-subgraphs. In 1987, Stiebitz proved Gallai's conjecture in the case k = 4, and in 1
## Abstract A graph __G__ is class II, if its chromatic index is at least Δ + 1. Let __H__ be a maximum Δ‐edge‐colorable subgraph of __G__. The paper proves best possible lower bounds for |__E__(__H__)|/|__E__(__G__)|, and structural properties of maximum Δ‐edge‐colorable subgraphs. It is shown tha