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Algorithmic Extensions of Dirac's Theorem on Long Cycles in Graphs with Large Minimum Vertex Degrees

The authors provide an algorithmic generalization of Dirac's theorem, showing that for a 2-connected graph G, deciding whether G contains a cycle of length at least min{2δ(G-B), |V(G)|-|B|} + k can be done in time 2^O(k+|B|) * n^O(1), where B is a subset of vertices and k is an integer.