Faktorizace kompletních grafů na pulce

Abstract

In this master thesis we investigate factorizations of complete graphs K_{4k+3} into tadpoles for k<=1 (a tadpole is a graph G that arise if we glue one terminal vertex of path of length |V(G)|-m to an arbitary vertex of cycle C_m for 3&lt;=m&lt;=|V(G)|-1).

We show that every tadpole with 4k+3 vertices factorizes a complete graph K_{4k+3} if lengths of cycles are m=3,4,...,2k+2,2k+4,..., 4k+2 for k odd resp. m=3,4,...,2k+1,2k+3,...,4k+2 for k even. We see that lengths of cylces m=2k+3 for k odd resp. m=2k+2 for k even are missing. Proofs of this lengths of cycles are not finished yet. But they will featured in the article that follows this thesis.