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arXiv · 2110.02013

Two Disjoint Alternating Paths in Bipartite Graphs

Archontia C. Giannopoulou·Sebastian Wiederrecht
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Abstract

A bipartite graph B is called a brace if it is connected and every matching of size at most two in B is contained in some perfect matching of B and a cycle C in B is called conformal if B-V(C) has a perfect matching. We show that there do not exist two disjoint alternating paths that form a cross over a conformal cycle C in a brace B if and only if one can reduce B, by an application of a matching theoretic analogue of small clique sums, to a planar brace H in which C bounds a face. We then utilise this result and provide a polynomial time algorithm which solves the 2-linkage problem for alternating paths in bipartite graphs with perfect matchings.

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Archontia C. Giannopoulou, Sebastian Wiederrecht. 2021-10-05. Two Disjoint Alternating Paths in Bipartite Graphs. https://arxiv.org/abs/2110.02013

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