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

## TL;DR

This paper proves that finite vertex-transitive graphs with a clique intersecting all maximal cliques are complete, providing insights into the evasiveness conjecture and answering questions posed by Berge and Payan.

## Contribution

It establishes a new characterization of vertex-transitive graphs with certain clique properties, advancing understanding of the evasiveness conjecture.

## Key findings

- Vertex-transitive graphs with intersecting maximal cliques are complete.
- Provides a positive answer to a case of the evasiveness conjecture.
- Addresses a question raised by Berge and Payan.

## 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.

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Source: https://tomesphere.com/paper/1703.10819