Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648617 | Discrete Mathematics | 2010 | 13 Pages |
Abstract
Let Cm[K¯2] stand for a cycle CmCm in which every vertex is replaced by two isolated vertices and every edge by K2,2K2,2. We prove that the complete graph K8mk+1K8mk+1 can be decomposed into graphs isomorphic to Cm[K¯2] for any m≥3m≥3, k>0k>0. Decompositions of complete graphs into certain collections of even cycles are obtained as a corollary. Also some special cases of Alspach Conjecture are solved in this article. All proofs are constructive and use both graph theory and design theory techniques.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Dalibor Fronček, Petr Kovář, Michael Kubesa,