Burr recently proved [3] that for positive integers m , , m 2 , . . , , m, and any graph G we have x(G) 5 &, if and only if G can be expressed as the edge disjoint union of subgraphs F, satisfying x(F,) 5 m,. This theorem is generalized to hypergraphs. By suitable interpretations the generalization
Chromatic number of finite and infinite graphs and hypergraphs
✍ Scribed by Paul Erdös; Andras Hajnal
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 349 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We wrote many papers on these subjects, some in collaboration with Galvin, Rado, Shelah and Szemer6di, and posed many problems some of which turned out to be undecidable. In this survey we state some old and new solved and unsolved problems.
Nous avons 6crit beaucoup d'articles, certains en collaboration avec Galvin, Rado, Shelah et Szemer6di, au sujet du hombre chromatique des graphes et des hypergraphes, finis ou infinis. Nous avons pos6 bien des probl~mes, dont certains se sont av6r6s ind6cidables. Darts cette br~ve synth~se nous pr6sentons quelques probl~mes, anciens ou r6cents, r6solus ou encore en suspens.
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