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. (~
Coloring perfect (K4 − e)-free graphs
✍ Scribed by Alan Tucker
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 349 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0095-8956
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We consider the question of the computational complexity of coloring perfect graphs with some precolored vertices. It is well known that a perfect graph can be colored optimally in polynomial time. Our results give a sharp border between the polynomial and NP-complete instances, when precolored vert
## Abstract We derive decomposition theorems for __P__~6~, __K__~1~ + __P__~4~‐free graphs, __P__~5~, __K__~1~ + __P__~4~‐free graphs and __P__~5~, __K__~1~ + __C__~4~‐free graphs, and deduce linear χ‐binding functions for these classes of graphs (here, __P__~__n__~ (__C__~__n__~) denotes the path