Outputs (4)

Unbalanced bipartite factorizations of complete bipartite graphs (2006)
Journal Article
Martin, N. (2006). Unbalanced bipartite factorizations of complete bipartite graphs. Discrete Mathematics, 306(17), 2084-2090. https://doi.org/10.1016/j.disc.2006.04.004

We construct a new infinite family of factorizations of complete bipartite graphs by factors all of whose components are copies of a (fixed) complete bipartite graph $K_{p,q}. There are simple necessary conditions for such factorizations to exist. Th... Read More about Unbalanced bipartite factorizations of complete bipartite graphs.

Unbalanced star-factorisations of complete bipartite graphs (2004)
Journal Article
Martin, N. (2004). Unbalanced star-factorisations of complete bipartite graphs. Discrete Mathematics, 283(1-3), 159-165. https://doi.org/10.1016/j.disc.2004.01.003

There are simple arithmetic conditions necessary for the complete bipartite graph Km;n to have a complete factorisation by subgraphs which are made up of disjoint copies of Kp;q. It is conjectured that these conditions are also su0cient (something al... Read More about Unbalanced star-factorisations of complete bipartite graphs.

Permutation separations and complete bipartite factorizations of Kn,n (2003)
Journal Article
Martin, N., & Stong, R. (2003). Permutation separations and complete bipartite factorizations of Kn,n. Electronic Journal of Combinatorics, 10(1),

Suppose p

Complete bipartite factorisations of Kn,n (2003)
Journal Article
Martin, N. (2003). Complete bipartite factorisations of Kn,n. Discrete Mathematics, 266(1-3), 353-375. https://doi.org/10.1016/s0012-365x%2802%2900819-1

We continue the study of complete factorisations of complete bipartite graphs of the form Kn,n by factors whose components are copies of Kp,q for given, fixed, p