On Existence of Must-Include Paths and Cycles in Undirected Graphs

02/19/2023

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by   Yefim Dinitz, et al.

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Given an undirected graph G=(V,E) and vertices s,t,w_1,w_2∈ V, we study finding whether there exists a simple path P from s to t such that w_1,w_2 ∈ P. As a sub-problem, we study the question: given an undirected graph and three of its edges, does there exist a simple cycle containing all those edges? We provide necessary and sufficient conditions for the existence of such paths and cycles, and develop efficient algorithms to solve this and related problems.