Triangle-free graphs with no six-vertex induced path
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Seymour, Paul | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.contributor.author | Zhong, Mingxian | |
| dc.date.accessioned | 2022-08-12T00:31:06Z | |
| dc.date.available | 2022-08-12T00:31:06Z | |
| dc.date.issued | 2018-08 | |
| dc.description | The final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2018.04.020. © 2018. 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 | The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced path. Here are three examples: the 16-vertex Clebsch graph, the graph obtained from an 8-cycle by making opposite vertices adjacent, and the graph obtained from a complete bipartite graph by subdividing a perfect matching. We show that every connected triangle-free graph with no six-vertex induced path is an induced subgraph of one of these three (modulo some twinning and duplication). | en |
| dc.description.sponsorship | This material is based upon work supported by, or in part by, the U.S. Army Research Laboratory and the U. S. Army Research Office under contract/grant number W911NF-16-1-0404, and supported by NSF Grant DMS-1550991. The second author was supported by ONR grant N00014-14-1-0084 and NSF grant DMS-1265563. | en |
| dc.identifier.uri | https://doi.org/10.1016/j.disc.2018.04.020 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18513 | |
| 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 | induced subgraph | en |
| dc.subject | induced path | en |
| dc.title | Triangle-free graphs with no six-vertex induced path | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Chudnovsky, M., Seymour, P., Spirkl, S., & Zhong, M. (2018). Triangle-free graphs with no six-vertex induced path. Discrete Mathematics, 341(8), 2179–2196. https://doi.org/10.1016/j.disc.2018.04.020 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |