Generalized local colorings of graphs
✍ Scribed by Miroslaw Truszczyński
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 649 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
Let G be a graph, m > r t> 1 integers. Suppose that it has a good-coloring with m colors which uses at most r colors in the neighborhood of every vertex. We investigate these so-called local r-colorings. One of our results (Theorem 2.4) states: The chromatic number of G, Chr(G) ~< r2" log21og2 m (an
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Given a property P, graph G. and k 2 0, a P k-coloring is a function 7r: V(G) + { I , ... , k) such that the subgraph induced by each color class has property P; x ( G : P ) is the least k, for which G has a P k-coloring. We investigate here the theory of P colorings. Generalizations of the wellknow
Suppose G is a graph embedded in S g with width (also known as edge width) at least 264(2 g À 1). If P V(G) is such that the distance between any two vertices in P is at least 16, then any 5-coloring of P extends to a 5-coloring of all of G. We present similar extension theorems for 6-and 7-chromati