Coloring graphs with no odd-K4
β Scribed by Wenan Zang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 350 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
The purpose of this note is to present a polynomial-time algorithm which, given an arbitrary graph G as its input, finds either a proper 3-coloring of G or an odd-K4 that is a subgraph of G in time O(mn), where m and n stand for the number of edges and the number of vertices of G, respectively. (~
π SIMILAR VOLUMES
The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N
An odd hole in a graph is an induced cycle of odd length at least five. In this article we show that every imperfect K 4 -free graph with no odd hole either is one of two basic graphs, or has an even pair or a clique cutset. We use this result to show that every K 4 -free graph with no odd hole has
Gyarf&, A., Graphs with k odd cycle lengths, Discrete Mathematics 103 (1992) 41-48. If G is a graph with k z 1 odd cycle lengths then each block of G is either KZk+2 or contains a vertex of degree at most 2k. As a consequence, the chromatic number of G is at most 2k + 2. For a graph G let L(G) deno
## Abstract In this paper we investigate the problem of cliqueβcoloring, which consists in coloring the vertices of a graph in such a way that no monochromatic maximal clique appears, and we focus on oddβholeβfree graphs. On the one hand we do not know any oddβholeβfree graph that is not 3βcliqueβc