Chorded pancyclic properties in claw-free graphs
| Author(s) | Beck, Kathryn | |
| Author(s) | Cenek, Lisa | |
| Author(s) | Cream, Megan | |
| Author(s) | Gelb, Brittany | |
| Date Accessioned | 2022-07-20T15:23:42Z | |
| Date Available | 2022-07-20T15:23:42Z | |
| Publication Date | 2022 | |
| Description | This article was originally published in The Australasian Journal of Combinatorics. The version of record is available at: https://ajc.maths.uq.edu.au/pdf/83/ajc_v83_p312.pdf | en_US |
| Abstract | A graph G is (doubly) chorded pancyclic if G contains a (doubly) chorded cycle of every possible length m for 4 ≤ m ≤ |V (G)|. In 2018, Cream, Gould, and Larsen completely characterized the pairs of forbidden subgraphs that guarantee chorded pancyclicity in 2-connected graphs. In this paper, we show that the same pairs also imply doubly chorded pancyclicity. We further characterize conditions for the stronger property of doubly chorded (k, m)-pancyclicity where, for k ≤ m ≤ |V (G)|, every set of k vertices in G is contained in a doubly chorded i-cycle for all m ≤ i ≤ |V (G)|. In particular, we examine forbidden pairs and degree sum conditions that guarantee this recently defined cycle property. | en_US |
| Sponsor | We are grateful to Ron Gould and the anonymous referees, whose detailed mathematical and stylistic comments helped us improve this paper. This work has been supported by NSF grant #1560222 at the Lafayette College REU. We thank Derek Smith and Liz McMahon for their support at the program. | en_US |
| Citation | Beck, Kathryn, Lisa Cenek, Megan Cream, and Brittany Gelb. “Chorded Pancyclic Properties in Claw-Free Graphs.” The Australasian Journal of Combinatorics 83, no. 3 (2022): 312–36. | en_US |
| ISSN | 2202-3518 | |
| URL | https://udspace.udel.edu/handle/19716/31130 | |
| Language | en_US | en_US |
| Publisher | The Australasian Journal of Combinatorics | en_US |
| Title | Chorded pancyclic properties in claw-free graphs | en_US |
| Type | Article | en_US |
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