Fractional Aspects of the Erdős-Faber-Lovász Conjecture

• Autorzy: John Bosica , Claude Tardif
• Języki publikacji: EN

Abstrakty

EN

The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lovász conjecture, involving variations of the fractional chromatic number. We exhibit some relaxations that can be proved in the spirit of the Kahn-Seymour result, and others that are equivalent to the original conjecture.

Słowa kluczowe

EN

Erdős-Faber-Lovász Conjecture; fractional chromatic number

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 1
• Strony: 197-202

Daty

wydano

2015-02-01

otrzymano

2013-05-22

poprawiono

2013-11-28

zaakceptowano

2014-02-20

online

2015-02-06

Twórcy

autor

John Bosica

• Department of Mathematics and Computer Science Royal Military College of Canada PO Box 17000 Stn Forces, Kingston, ON Canada, K7K 7B4

autor

Claude Tardif

• Department of Mathematics and Computer Science Royal Military College of Canada PO Box 17000 Stn Forces, Kingston, ON Canada, K7K 7B4

Bibliografia

• [1] N.G. de Bruijn and P. Erdős, On a combinatorial problem, Nederl. Akad. Wetensch.
• Indag. Math 10 (1948) 421-423.
• [2] P. Erdős, R.C. Mullin, V.T. Sos and D.R. Stinson, Finite linear spaces and projective planes, Discrete Math. 47 (1983) 49-62. doi:10.1016/0012-365X(83)90071-7[Crossref]
• [3] J. Kahn, Coloring nearly-disjoint hypergraphs with n+o(n) colors, J. Combin. The- ory (A) 59 (1992) 31-39. doi:10.1016/0097-3165(92)90096-D[Crossref]
• [4] J. Kahn and P.D. Seymour, A fractional version of the Erdős-Faber-Lovász conjec- ture, Combinatorica 12 (1992) 155-160. doi:10.1007/BF01204719[Crossref]
• [5] E.R. Scheinerman and D.H. Ullman, Fractional Graph Theory (Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York, 1997).

Identyfikatory

DOI

10.7151/dmgt.1781