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Multicolored forests in complete bipartite graphs
Authors:Richard A Brualdi and Susan Hollingsworth
Institution:

Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706-1388, USA

Abstract:If the edges of a graph G are colored using k colors, we consider the color distribution for this coloring a=(a1,a2,…,ak), in which ai denotes the number of edges of color i for i=1,2,…,k. We find inequalities and majorization conditions on color distributions of the complete bipartite graph Kn,n which guarantee the existence of multicolored subgraphs: in particular, multicolored forests and trees. We end with a conjecture on partitions of Kn,n into multicolored trees.
Keywords:Complete bipartite graph  Majorization  Multicolored subgraphs  Trees
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