@Article{Froncek2010,
author = "Froncek, Dalibor",
title = "Decomposition of complete graphs into small graphs",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "3",
pages = "277--280",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.3.277",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.3.277",
abstract = "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 \(K_{km}\).",
keywords = "graph decomposition, graph labeling",
issn = "1232-9274"
}