A note on graphs with disjoint maximal cliques ans a link with evasiveness

Abstract

In this note, we prove that a finite vertex-transitive graph which has a clique which intersects all maximal cliques is a complete graph. This gives a positive answer in the case of vertex-transitive graphs to a question raised by Berge and Payan. It also gives a positive answer to a special case of the evasiveness conjecture.

There is an error in the proof of Lemma 2 which affects the Theorems 1 and 3. In the actual state, the main claim (see abstract) remains unproved. 9 pages, 2 figures