Erdos-Faber-Lovász conjecture

In graph theory, the Erdős-Faber-Lovász conjecture (1972) is a very deep problem about the coloring of graphs. It says:

The union of k copies of k-cliques intersecting in at most one vertex pairwise is k-chromatic.

Erdős originally offered US$50 for proving the conjecture in the affirmative, and later raised the reward to US$500. It is easy to show that the desired chromatic number is less than <math>1 + k \sqrt{k – 1}<math>.

See also

• Erdős conjecture

References

• Erdős, Paul (1981). On the combinatorial problems I would most like to see solved. Combinatorica 1, 25–42.