English

Spanning trails with maximum degree at most 4 in $2K_2$-free graphs

Combinatorics 2016-09-29 v1

Abstract

A graph is called 2K22K_2-free if it does not contain two independent edges as an induced subgraph. Mou and Pasechnik conjectured that every 32\frac{3}{2}-tough 2K22K_2-free graph with at least three vertices has a spanning trail with maximum degree at most 44. In this paper, we confirm this conjecture. We also provide examples for all t<54t < \frac{5}{4} of tt-tough graphs that do not have a spanning trail with maximum degree at most 44.

Keywords

Cite

@article{arxiv.1609.08730,
  title  = {Spanning trails with maximum degree at most 4 in $2K_2$-free graphs},
  author = {Guantao Chen and M. N. Ellingham and Akira Saito and Songling Shan},
  journal= {arXiv preprint arXiv:1609.08730},
  year   = {2016}
}
R2 v1 2026-06-22T16:03:37.873Z