# Mount Saint Mary College Authors

ARTICLES

Title:(k,g)-cages are 3-connected
Authors:Michael Daven
Periodical:Discrete Mathematics, v199, 1999, p207-215

Title:The Johnson graph has connectivity $\delta$
Authors:Michael Daven
Periodical:Proceedings of the 30th Southeastern International Conference on Combinatorics, Graph Theory, & Computing, Boca Raton, 1999, p123-128

Title:Maximal sets of hamilton cycles in complete multipartite graphs
Authors:Michael Daven
Periodical:Discrete Mathematics, v43, 2003, p49-66

Title:Multidesigns for graph-pairs of order 4 and 5
Authors:Michael Daven
Periodical:Graphs & Combinatorics, v19, n4, 2003, p433-447
Absgtract:The graph decomposition problem is well known. We say a subgraph G divides K m if the edges of K m can be partitioned into copies of G. Such a partition is called a G-decomposition or G-design. The graph multidecomposition problem is a variation of the above. By a graph-pair of order t, we mean two non-isomorphic graphs G and H on t non-isolated vertices for which GHK t for some integer t4. Given a graph-pair (G,H), if the edges of K m can be partitioned into copies of G and H with at least one copy of G and one copy of H, we say (G,H) divides K m . We will refer to this partition as a (G,H)-multidecomposition. In this paper, we consider the existence of multidecompositions for several graph-pairs. For the pairs (G,H) which satisfy GHK 4 or K 5, we completely determine the values of m for which K m admits a (G,H)-multidecomposition. When K m does not admit a (G,H)-multidecomposition, we instead find a maximum multipacking and a minimum multicovering. A multidesign is a multidecomposition, a maximum multipacking, or a minimum multicovering.

Title:Multidecompositions of the complete graph
Authors:Michael Daven
Periodical:Ars Combinitoria, vLXXII, 2004, p17-22

Title:Multidesigns of the $\lambda$-fold complete graph for graph-pairs of orders 4 and 5
Authors:Michael Daven
Periodical:Australasian Journal of Combinatorics, v32, June 2005, p125-136

Title:Multidesigns for graph-triples of order 6
Authors:Michael Daven
Periodical:Congressus Numerantium, v183, 2006, p139-160