Hajós' theorem for list colorings of hypergraphs

Claude Benzaken; Sylvain Gravier; Riste Skrekovski

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 2, page 207-213
  • ISSN: 2083-5892

Abstract

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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 K k + 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.

How to cite

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Claude Benzaken, Sylvain Gravier, and Riste Skrekovski. "Hajós' theorem for list colorings of hypergraphs." Discussiones Mathematicae Graph Theory 23.2 (2003): 207-213. <http://eudml.org/doc/270536>.

@article{ClaudeBenzaken2003,
abstract = {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 $K_\{k+1\}$ 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.},
author = {Claude Benzaken, Sylvain Gravier, Riste Skrekovski},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {list-coloring; Hajós' construction; hypergraph; list coloring; Hajós’ theorem},
language = {eng},
number = {2},
pages = {207-213},
title = {Hajós' theorem for list colorings of hypergraphs},
url = {http://eudml.org/doc/270536},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Claude Benzaken
AU - Sylvain Gravier
AU - Riste Skrekovski
TI - Hajós' theorem for list colorings of hypergraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 2
SP - 207
EP - 213
AB - 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 $K_{k+1}$ 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.
LA - eng
KW - list-coloring; Hajós' construction; hypergraph; list coloring; Hajós’ theorem
UR - http://eudml.org/doc/270536
ER -

References

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  1. [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. Zbl0397.05038
  2. [2] C. Benzaken, Hajós' theorem for hypergraphs, Annals of Discrete Math. 17 (1983) 53-77. 
  3. [3] P. Erdős, A.L. Rubin, and H. Taylor, Choosability in graphs, Congr. Numer. 26 (1980) 122-157. Zbl0469.05032
  4. [4] S. Gravier, A Hajós-like theorem for list colorings, Discrete Math. 152 (1996) 299-302, doi: 10.1016/0012-365X(95)00350-6. Zbl0853.05037
  5. [5] G. Hajós, Über eine Konstruktion nicht n-färbbarer Graphen, Wiss. Z. Martin Luther Univ. Math.-Natur. Reihe 10 (1961) 116-117. 
  6. [6] B. Mohar, Hajós theorem for colorings of edge-weighted graphs, manuscript, 2001. 
  7. [7] V.G. Vizing, Colouring the vertices of a graph in prescribed colours (in Russian), Diskret. Anal. 29 (1976) 3-10. 
  8. [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. Zbl0971.05042

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