Cayley snarks and almost simple groups

Nedela, Roman, 1960- Cayley snarks and almost simple groups / R. Nedela, M. Skoviera. -- 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.

In Combinatorica. -- Heidelberg : Springer-Verlag, 1981-. -- ISSN 0209-9683. -- ISSN 1439-6912. -- Vol. 21, no. 4 (2001), pp. 583-590

1. matematika 2. grafy

I. Škoviera, Martin
II. Combinatorica. -- Vol. 21, no. 4 (2001), pp. 583-590

51
BB301