Vertex-transitive graphs that have no Hamilton decomposition
arXiv:1408.5211
Abstract
It is shown that there are infinitely many connected vertex-transitive graphs that have no Hamilton decomposition, including infinitely many Cayley graphs of valency 6, and including Cayley graphs of arbitrarily large valency.
This version includes observations that some more of our graphs are Cayley graphs, and some revisions with new notation. It also includes some additional concluding remarks, and some updating of references
References in corpus (3)
- Proof of the 1-factorization and Hamilton decomposition conjectures II: the bipartite case
- Proof of the 1-factorization and Hamilton decomposition conjectures III: approximate decompositions
- Proof of the 1-factorization and Hamilton decomposition conjectures IV: exceptional systems for the two cliques case