Geodesic
Fractional Aspects of the Erdős-Faber-Lovász Conjecture
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 197-202 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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.
Keywords: Erdős-Faber-Lovász Conjecture, fractional chromatic number 
@article{DMGT_2015_35_1_a15,
     author = {Bosica, John and Tardif, Claude},
     title = {Fractional {Aspects} of the {Erd\H{o}s-Faber-Lov\'asz} {Conjecture}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {197--202},
     year = {2015},
     volume = {35},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a15/}
}
TY  - JOUR
AU  - Bosica, John
AU  - Tardif, Claude
TI  - Fractional Aspects of the Erdős-Faber-Lovász Conjecture
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2015
SP  - 197
EP  - 202
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a15/
LA  - en
ID  - DMGT_2015_35_1_a15
ER  - 
%0 Journal Article
%A Bosica, John
%A Tardif, Claude
%T Fractional Aspects of the Erdős-Faber-Lovász Conjecture
%J Discussiones Mathematicae. Graph Theory
%D 2015
%P 197-202
%V 35
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a15/
%G en
%F DMGT_2015_35_1_a15
Bosica, John; Tardif, Claude. Fractional Aspects of the Erdős-Faber-Lovász Conjecture. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 197-202. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a15/

[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

[3] J. Kahn, Coloring nearly-disjoint hypergraphs with n+o(n) colors, J. Combin. Theory (A) 59 (1992) 31-39. doi:10.1016/0097-3165(92)90096-D

[4] J. Kahn and P.D. Seymour, A fractional version of the Erdős-Faber-Lovász conjecture, Combinatorica 12 (1992) 155-160. doi:10.1007/BF01204719

[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).