If the edges of a complete graph K,., m/> 4, are painted two colours so that monochromatic K " graphs are connected, then there exists an increasing sequence ( n)n~4 of complete subgraphs whose monochromatic subgraphs are also connected. For more than two colours this is not true, but an analogous f
NP-completeness of edge-colouring some restricted graphs
β Scribed by Leizhen Cai; John A. Ellis
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 850 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0166-218X
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## Abstract We show that the following problem is __NP__ complete: Let __G__ be a cubic bipartite graph and __f__ be a precoloring of a subset of edges of __G__ using at most three colors. Can __f__ be extended to a proper edge 3βcoloring of the entire graph __G__? This result provides a natural co
We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the follou~ng conjecture by B. Bollobis and P. Erdijs (1976): if G is an edge-coloured complete graph on )I vertices in which the max