UVictoria Discrete Math Seminar: Peter Dukes

An F-decomposition of a graph G is a set of subgraphs of G, each isomorphic to F, whose edge sets partition the edge set of G. I will speak about a result showing that, for each odd k ≥ 5, any graph G of sufficiently large order n with minimum degree at least (1/2+1/(2k-4)+o(1))n has a C_k-decomposition if and only if k divides |E(G)| and all vertex degrees in G are even. Our methodology also leads to results on F-decompositions for other 3-partite graphs F. This is joint work with Darryn Bryant, Daniel Horsley, Barbara Maenhaut and Richard Montgomery.