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Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs

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minimal.pdf (122.25 KB)

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

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Citation

URI

https://doi.org/10.1016/j.disc.2022.112869
 http://hdl.handle.net/10012/18595

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Waterloo Research
Combinatorics and Optimization