Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs
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Date
2022-07
Authors
Cheriyan, Joseph
Hajebi, Sepehr
Qu, Zishen
Spirkl, Sophie
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
In 1981, Duffus, Gould, and Jacobson showed that every connected graph either has a Hamiltonian path, or contains a claw (K1,3) or a net (a fixed six-vertex graph) as an induced subgraph. This implies that subject to being connected, these two are the only minimal (under taking induced subgraphs) graphs with no Hamiltonian path.
Brousek (1998) characterized the minimal graphs that are 2-connected, non-Hamiltonian and do not contain the claw as an induced subgraph. We characterize the minimal graphs that are 2-connected and non-Hamiltonian for two classes of graphs: (1) split graphs, (2) triangle-free graphs. We remark that testing for Hamiltonicity is NP-hard in both classes.
Description
The final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2022.112869. © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
Hamiltonicity, induced subgraphs, split graphs