Cayley Snarks and Almost Simple Groups |
| |
Authors: | Roman Nedela Martin Škoviera |
| |
Institution: | (1) School of Finance, M. Bel University; 975 49 Banská Bystrica, Slovakia, SK;(2) Department of Computer Science, Faculty of Mathematics and Physics, Comenius University; 842 15 Bratislava, Slovakia; E-mail: skoviera@dcs.fmph.uniba.sk, SK |
| |
Abstract: | 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.
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 |
| |
Keywords: | AMS Subject Classification (2000) Classes: 05C25 05C15 05C10 |
本文献已被 SpringerLink 等数据库收录! |
|