Cayley Snarks and Almost Simple Groups

A Cayley snark is a cubic Cayley graph which is not 3-edge-colourable. In the paper we discuss the problem of the existence of Cayley snarks. This problem is closely related to the problem of the existence of non-hamiltonian Cayley graphs and to the question whether every Cayley graph admits a nowhere-zero 4-flow.

So far, no Cayley snarks have been found. On the other hand, we prove that the smallest example of a Cayley snark, if it exists, comes either from a non-abelian simple group or from a group which has a single non-trivial proper normal subgroup. The subgroup must have index two and must be either non-abelian simple or the direct product of two isomorphic non-abelian simple groups.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Additional information

Received January 18, 2000

Research partially supported by VEGA grant 1/3213/96

Research partially supported by VEGA grants 1/3213/96 and 1/4318/97

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nedela, R., Škoviera, M. Cayley Snarks and Almost Simple Groups. Combinatorica 21, 583–590 (2001). https://doi.org/10.1007/s004930100014

Download citation

  • AMS Subject Classification (2000) Classes:  05C25, 05C15, 05C10