Decomposition of complete graphs into C_m[2]

Constructive proof that all pompous cycle decompositions of K_8mk+1 exist.

Abstract

We prove that the complete graph K_8mk+1 can be decomposed into graphs isomorphic to C_m[2] (called pompous cycle) for any m,k>0. All proofs are constructive and use both graph theory and design theory techniques.

Status

Accepted for publication in a special volume of Discrete mathematics (DM) entitled "Topics in Discrete Mathematics". The volume contains selected papers from the 6th Czech-Slovak International Symposium in Combinatorics, Graph Theory Algorithms and Applications, which has been held in Prague in July 2006.
D. Fronček, P. Kovář and M. Kubesa, Decomposition of complete graphs into C_m[2], accepted. (DM)

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Last update: 29.12.2011