Reconfiguring Hamiltonian Cycles in L-Shaped Grid Graphs

Abstract

Given a pair of 1-complex Hamiltonian cycles C and $$C'$$ in an L-shaped grid graph G, we show that one is reachable from the other under two operations, flip and transpose, while remaining in the family of 1-complex Hamiltonian cycles throughout the reconfiguration. Operations flip and transpose are local in G. We give a reconfiguration algorithm that uses O(|G|) operations.