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

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.

READ FULL TEXT