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arXiv · 1511.02038

2-Trees: Structural Insights and the study of Hamiltonian Paths

P. Renjith·N. Sadagopan
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Abstract

For a connected graph, a path containing all vertices is known as \emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a Hamiltonian path in general graphs is NP-Complete. We present a necessary and sufficient condition for the existence of Hamiltonian paths in 2-trees. Using our characterization, we also present a linear-time algorithm for the existence of Hamiltonian paths in 2-trees. Our characterization is based on a deep understanding of the structure of 2-trees and the combinatorics presented here may be used in other combinatorial problems restricted to 2-trees.

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P. Renjith, N. Sadagopan. 2016-07-20. 2-Trees: Structural Insights and the study of Hamiltonian Paths. https://arxiv.org/abs/1511.02038

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