Hamiltonicity in Semi-Regular Tessellation Dual Graphs
Divya Gopinath, Rohan Kodialam, Kevin Lu, Jayson Lynch, Santiago, Ospina
TL;DR
This paper proves that finding Hamiltonian cycles is NP-complete in dual graphs of semi-regular tessellations and NP-hard in augmented square grids, extending the understanding of computational complexity in grid-like graphs.
Contribution
It establishes NP-completeness and NP-hardness results for Hamiltonian cycle problems in new classes of semi-regular tessellation dual graphs and augmented square grids.
Findings
NP-completeness for dual graphs of semi-regular tessellations
NP-hardness for augmented square grids
Extends complexity results to new grid graph classes
Abstract
This paper shows NP-completeness for finding Hamiltonian cycles in induced subgraphs of the dual graphs of semi-regular tessilations. It also shows NP-hardness for a new, wide class of graphs called augmented square grids. This work follows up on prior studies of the complexity of finding Hamiltonian cycles in regular and semi-regular grid graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Graph theory and applications