ON THE RELATIONSHIP BETWEEN GRAPHS AND TOTALLY POSITIVE MATRICES #
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by J. M. Pe Na
http://epubs.siam.org/sam-bin/getfile/SIMAX/articles/30396.ps.Z
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Abstract:
Abstract. A real matrix is said to be totally positive if all its minors are nonnegative. In this paper it is shown that properties of totally positive matrices can be applied to graph theory, and conversely. In fact, some properties of undirected and directed graphs (digraphs) are characterized in terms of the associated totally positive matrices. Some results on the existence of nonintersecting paths in a digraph are also provided.
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