Hajós' theorem for list colorings of hypergraphs
Claude Benzaken ; Sylvain Gravier ; Riste Skrekovski
Discussiones Mathematicae Graph Theory, Tome 23 (2003), p. 207-213 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

A well-known theorem of Hajós claims that every graph with chromathic number greater than k can be constructed from disjoint copies of the complete graph Kk+1 by repeated application of three simple operations. This classical result has been extended in 1978 to colorings of hypergraphs by C. Benzaken and in 1996 to list-colorings of graphs by S. Gravier. In this note, we capture both variations to extend Hajós’ theorem to list-colorings of hypergraphs.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:270536 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1197,
     author = {Claude Benzaken and Sylvain Gravier and Riste Skrekovski},
     title = {Haj\'os' theorem for list colorings of hypergraphs},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {23},
     year = {2003},
     pages = {207-213},
     zbl = {1054.05035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1197}
}

Claude Benzaken; Sylvain Gravier; Riste Skrekovski. Hajós' theorem for list colorings of hypergraphs. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 207-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1197/

[000] [1] C. Benzaken, Post's closed systems and the weak chromatic number of hypergraphs, Discrete Math. 23 (1978) 77-84, doi: 10.1016/0012-365X(78)90106-1. | Zbl 0397.05038

[001] [2] C. Benzaken, Hajós' theorem for hypergraphs, Annals of Discrete Math. 17 (1983) 53-77.

[002] [3] P. Erdős, A.L. Rubin, and H. Taylor, Choosability in graphs, Congr. Numer. 26 (1980) 122-157. | Zbl 0469.05032

[003] [4] S. Gravier, A Hajós-like theorem for list colorings, Discrete Math. 152 (1996) 299-302, doi: 10.1016/0012-365X(95)00350-6. | Zbl 0853.05037

[004] [5] G. Hajós, Über eine Konstruktion nicht n-färbbarer Graphen, Wiss. Z. Martin Luther Univ. Math.-Natur. Reihe 10 (1961) 116-117.

[005] [6] B. Mohar, Hajós theorem for colorings of edge-weighted graphs, manuscript, 2001.

[006] [7] V.G. Vizing, Colouring the vertices of a graph in prescribed colours (in Russian), Diskret. Anal. 29 (1976) 3-10.

[007] [8] X. Zhu, An analogue of Hajós's theorem for the circular chromatic number, Proc. Amer. Math. Soc. 129 (2001) 2845-2852, doi: 10.1090/S0002-9939-01-05908-1. | Zbl 0971.05042