Opuscula Math. 30, no. 3 (2010), 277-280

Opuscula Mathematica

Decomposition of complete graphs into small graphs

Dalibor Froncek

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.

Mathematics Subject Classification: 05C78.

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  • Dalibor Froncek
  • University of Minnesota, Duluth, Department of Mathematics and Statistics, 1117 University Dr., Duluth, MN 55812, U.S.A.
  • Received: 2010-01-21.
  • Accepted: 2010-03-26.
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Cite this article as:
Dalibor Froncek, Decomposition of complete graphs into small graphs, Opuscula Math. 30, no. 3 (2010), 277-280, http://dx.doi.org/10.7494/OpMath.2010.30.3.277

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