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Hamiltonian properties of triangular grid graphs. (English) Zbl 1158.05040
Summary: A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. In 2000, J.R. Reay and T. Zamfirescu [Discrete Comput. Geom. 24, No. 2-3, 497–502 (2000; Zbl 0953.05040)] showed that all 2-connected, linearly-convex triangular grid graphs (with the exception of one of them) are hamiltonian. The only exception is a graph \(D\) which is the linearly-convex hull of the Star of David. We extend this result to a wider class of locally connected triangular grid graphs. Namely, we prove that all connected, locally connected triangular grid graphs (with the same exception of graph \(D\)) are hamiltonian. Moreover, we present a sufficient condition for a connected graph to be fully cycle extendable. We also show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs.

MSC:
05C45 Eulerian and Hamiltonian graphs
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
92C40 Biochemistry, molecular biology
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