A deterministic linear-time algorithm finds an odd cycle through two specified vertices in an undirected graph, or more generally two cycles with distinct labels through two specified vertices or edges in a Γ-labeled graph where every element of Γ has order at most 2.
Finding a shortest non-zero path in group-labeled graphs.Combinatorica, 42(Suppl 2):1253–1282, 2022
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A Linear-Time Algorithm for Finding an Odd Cycle Through Two Specified Vertices
A deterministic linear-time algorithm finds an odd cycle through two specified vertices in an undirected graph, or more generally two cycles with distinct labels through two specified vertices or edges in a Γ-labeled graph where every element of Γ has order at most 2.