Note on the colouring of graphs
β Scribed by G. A. Dirac
- Publisher
- Springer-Verlag
- Year
- 1951
- Tongue
- French
- Weight
- 400 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
In this note we summarize some of the progress made recently by the author, A.G. Chetwynd and P.D. Johnson about edge-eolourings of graphs with relatively large maximum degree. In this note, multigraphs will have no loops. For a multigraph G, the least number of colours needed to colour the edges o
Grossman and Ha ggkvist gave a sufficient condition under which a two-edgecoloured graph must have an alternating cycle (i.e., a cycle in which no two consecutive edges have the same colour). We extend their result to edge-coloured graphs with any number of colours. That is, we show that if there is
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