Geodesic
On a Conjecture of Erdös, Faber, and Lovász about n-Colorings
Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 563-570

Voir la notice de l'article provenant de la source Cambridge University Press

Let be a finite family of finite sets with the property that |A ∩ B| ≦ 1 whenever A and B are distinct members of . It is a conjecture of Erdös, Faber, and Lovász ([1] a 50 pound problem and [2] a 100 dollar problem) that there is an n-coloring of (i.e., a function such that A ∩ B = ∅ whenever A and B are distinct members of with f(A) = f(B). They actually state the conjecture in a different form. They actually state the conjecture in a different form. Namely, if n is a positive integer and is a family of n sets satisfying (1) |Bp | = n for each p and (2) |Bp ∩ Bq | ≦ 1 when p ≠ q, then there is an n-coloring of the elements of so that each set Bp gets all n colors. The equivalence of the two forms is easily seen by interchanging the roles of elements and sets. 
Hindman, Neil. On a Conjecture of Erdös, Faber, and Lovász about n-Colorings. Canadian journal of mathematics, Tome 33 (1981) no. 3, pp. 563-570. doi: 10.4153/CJM-1981-046-9
@article{10_4153_CJM_1981_046_9,
     author = {Hindman, Neil},
     title = {On a {Conjecture} of {Erd\"os,} {Faber,} and {Lov\'asz} about {n-Colorings}},
     journal = {Canadian journal of mathematics},
     pages = {563--570},
     year = {1981},
     volume = {33},
     number = {3},
     doi = {10.4153/CJM-1981-046-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-046-9/}
}
TY  - JOUR
AU  - Hindman, Neil
TI  - On a Conjecture of Erdös, Faber, and Lovász about n-Colorings
JO  - Canadian journal of mathematics
PY  - 1981
SP  - 563
EP  - 570
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-046-9/
DO  - 10.4153/CJM-1981-046-9
ID  - 10_4153_CJM_1981_046_9
ER  - 
%0 Journal Article
%A Hindman, Neil
%T On a Conjecture of Erdös, Faber, and Lovász about n-Colorings
%J Canadian journal of mathematics
%D 1981
%P 563-570
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1981-046-9/
%R 10.4153/CJM-1981-046-9
%F 10_4153_CJM_1981_046_9

[1] 1. Erdos, P., Problems and results in graph theory and combinatorial analysis, Proceedings of the Fifth British Combinatorial Conference, 169-92. Congressus Numerantium, No. XV, Utilitas Math. (1976). Google Scholar

[2] 2. Erdos, P., Some recent problems and results on graph theory, combinatorics and number theory, Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory and Computing, 3-14. Congressus Numerantium, No. XVII, Utilitas Math. (1976). Google Scholar

Cité par Sources :