Decomposition of complete graphs into small graphs

Opuscula Mathematica

Dalibor Froncek¹ 

[1] University of Minnesota, Duluth, Department of Mathematics and Statistics, 1117 University Dr., Duluth, MN 55812, U.S.A.;

关键词: graph decomposition;    graph labeling;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2010.30.3.277

来源: DOAJ

【 摘 要 】

In 1967, A. Rosa proved that if a bipartite graph \(G\) with \(n\) edges has an \(\alpha\)-labeling, then for any positive integer \(p\) the complete graph \(K_{2np+1}\) can be cyclically decomposed into copies of \(G\). This has become a part of graph theory folklore since then. In this note we prove a generalization of this result. We show that every bipartite graph \(H\) which decomposes \(K_k\) and \(K_m\) also decomposes \(K_{km}\).

【 授权许可】

Unknown