$m$-Cycle Packings of $(\lambda +\mu )K_{v+u}-\lambda K_v$: $m$ even

Abstract

A $\lambda K_v$ is a complete graph on $v$ vertices with $\lambda$ edges between each pair of the $v$ vertices. A $(\lambda +\mu )K_{v+u}-\lambda K_v$ is a $(\lambda +\mu )K_{v+u}$ with the edge set of $\lambda K_v$ removed. Decomposing a $(\lambda +\mu )K_{v+u}-\lambda K_v$ into edge-disjoint $m$-cycles has been studied by many people. To date, there is a complete solution for $m=4$ and partial results when $m=3$ or $m=5$. In this paper, we are able to solve this problem for all even cycle lengths as long as $u,v\ge m+2$.

arXiv commentarXiv admin note: text overlap with arXiv:1204.3368 by other authors