Spanning closed trail and hamiltonian cycle in grid graphs
In this paper we study a trail routing and a hamiltonian cycle in a class of grid graphs, polycube and polymino. A Spanning closed trail is an eulerian subgraph containing all vertices of a given graph. For general grid graphs we prove that the problem of finding that trail is N P-complete and for a wide subclass of grid graphs, called polymino, we give an an optimal algorithm if it exists. For polycube graphs we prove that every polycube has a spanning closed trail. Finally we show that a graph product G to a simple path with length n, G × Pn, is hamiltonian for all n≥2, if G is a polymino with a perfect matching.
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