2015/11/30 by John Asplund, Asplund, John
Mathematics · #05C51 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C51
paper · pdf · doi:10.48550/arxiv.1511.09301
arXiv admin note: text overlap with arXiv:1204.3368 by other authors
arxiv created 2016/02/04 · arxiv updated 2016/02/05
A λKv is a complete graph on v vertices with λ edges between each pair of the v vertices. A (λ+μ)Kv+u-λKv is a (λ+μ)Kv+u with the edge set of λKv removed. Decomposing a (λ+μ)Kv+u-λKv 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≥ m+2.