TY  - JOUR
ID  - Froncek2010
LB  - Froncek2010
AU  - Froncek, Dalibor
TI  - Decomposition of complete graphs into small graphs
ST  - Decomposition of complete graphs into small graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 277
EP  - 280
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.277
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.277
AB  - 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 \(K_{km}\).
KW  - graph decomposition
KW  - graph labeling
SN  - 1232-9274
ER  -