Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs
| dc.contributor.author | Cheriyan, Joseph | |
| dc.contributor.author | Hajebi, Sepehr | |
| dc.contributor.author | Qu, Zishen | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-08-22 14:38:35 (GMT) | |
| dc.date.available | 2022-08-22 14:38:35 (GMT) | |
| dc.date.issued | 2022-07 | |
| dc.identifier.uri | https://doi.org/10.1016/j.disc.2022.112869 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18595 | |
| dc.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/ | en |
| dc.description.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. | en |
| dc.description.sponsorship | We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) [funding reference numbers RGPIN-2019-04197 and RGPIN-2020-03912]. | en |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | Hamiltonicity | en |
| dc.subject | induced subgraphs | en |
| dc.subject | split graphs | en |
| dc.title | Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Cheriyan, J., Hajebi, S., Qu, Z., & Spirkl, S. (2022). Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs. Discrete Mathematics, 345(7), 112869. https://doi.org/10.1016/j.disc.2022.112869 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Combinatorics and Optimization | en |
| uws.typeOfResource | Text | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
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