论文信息 - The rank and size of graphs

The rank and size of graphs

We show that the number of points with pairwise different sets of neighbors in a graph is O(2r/2), where r is the rank of the adjacency matrix. We also give an example that achieves this bound. © 1996 John Wiley & Sons, Inc.

László Lovász | Andrew Kotlov

[1] A. A. Razborov,et al. The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear , 1992, Discret. Math..

[2] Andreǐ Kotlov. Rank and chromatic number of a graph , 1997 .

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

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

[5] Ran Raz,et al. On the "log rank"-conjecture in communication complexity , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[6] Noga Alon,et al. A counterexample to the rank-coloring conjecture , 1989, J. Graph Theory.