Chorded pancyclic properties in claw-free graphs
Date
2022
Journal Title
Journal ISSN
Volume Title
Publisher
The Australasian Journal of Combinatorics
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.
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
Keywords
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.