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Article

Homomorphisms of binary Cayley graphs.

Discrete Mathematics. 2015. Vol. 338. No. 12. P. 2539-2544.
Beaudou L., Naserasr R., Tardif C.

A binary Cayley graph is a Cayley graph based on a binary group. In 1992, Payan proved that any non-bipartite binary Cayley graph must contain a generalized Mycielski graph of an odd cycle, implying that such a graph cannot have chromatic number 3.

We strengthen this result first by proving that any non-bipartite binary Cayley graph must contain a projective cube as a subgraph. We further conjecture that any homomorphism of a non-bipartite binary Cayley graph to a projective cube must be surjective and we prove a special case of this conjecture.