A conjectured bound on the spanning tree number of bipartite graphs

Slone, Michael

doi:10.48550/arxiv.1608.01929

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A Reformulation In Terms Of Majorization1

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2018

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“…In 2009, Jack Schmidt (as reported in [22]) computationally verified by an exhaustive search that all bipartite graphs on at most 13 vertices are Ferrers-good. For a bipartite graph, we refer to the vertices in the two parts as red vertices and blue vertices.…”

Section: A Reformulation In Terms Of Majorizationmentioning

confidence: 98%

Maximizing Spectral Radius and Number of Spanning Trees in Bipartite Graphs

Bapat

2018

Indian Statistical Institute Series

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The problems of maximizing the spectral radius and the number of spanning trees in a class of bipartite graphs with certain degree constraints are considered. In both the problems, the optimal graph is conjectured to be a Ferrers graph. Known results towards the resolution of the conjectures are described. We give yet another proof of a formula due to Ehrenborg and van Willigenburg for the number of spanning trees in a Ferrers graph. The main tool is a result which gives several necessary and sufficient conditions under which the removal of an edge in a graph does not affect the resistance distance between the end-vertices of another edge.

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Section: A Reformulation In Terms Of Majorizationmentioning

confidence: 98%