论文信息 - A counterexample to the rank-coloring conjecture

A counterexample to the rank-coloring conjecture

It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adja- cency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.

Noga Alon | Paul D. Seymour | N. Alon | P. Seymour

[1] Siemion Fajtlowicz,et al. On conjectures of Graffiti , 1988, Discret. Math..

[2] L. Lovász. Combinatorial problems and exercises , 1979 .

[3] C. V. Nuffelen,et al. A Bound for the Chromatic Number of a Graph , 1976 .