Uniquely colourable m-dichromatic oriented graphs
β Scribed by V Neumann-Lara; N Santoro; J Urrutia
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 362 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
For a graph G, the path number r(G) is defined as the order of a longest path in G. An (m, k)~-colouring of a graph H is a partition of the vertex set of H into m subsets such that each subset induces a subgraph of H for which r is at most k. The k -z-chromatic number z~(H) is the least m for which
The Clique-Pair-Conjecture (CPC) states that a uniquely colourable perfect graph, different from a clique, contains two maximum size cliques having a two element symmetric difference. One can make an auxiliary graph B from a minimal counterexample for the CPC (if any exists), this B is bipartite. We
This paper proves that if a graph G has an orientation D such that for each cycle C with djCj Γ°mod kΓ 2 f1; 2; . . . ; 2d Γ 1g we have jCj=jC ΓΎ j4k=d and jCj=jC Γ j4k=d; then G has a Γ°k; dΓ-colouring and hence w c Γ°GΓ4k=d: This is a generalization of a result of Tuza (J. Combin. Theory Ser. B 55 (19