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Sublinear Longest Path Transversals

Combinatorics 2025-04-23 v2 Discrete Mathematics

Abstract

We show that connected graphs admit sublinear longest path transversals. This improves an earlier result of Rautenbach and Sereni and is related to the fifty-year-old question of whether connected graphs admit longest path transversals of constant size. The same technique allows us to show that 22-connected graphs admit sublinear longest cycle transversals.

Keywords

Cite

@article{arxiv.2005.02716,
  title  = {Sublinear Longest Path Transversals},
  author = {James A. Long and Kevin G. Milans and Andrea Munaro},
  journal= {arXiv preprint arXiv:2005.02716},
  year   = {2025}
}

Comments

A previous version of this arXiv post has been split into two parts; this is the first of the two parts

R2 v1 2026-06-23T15:20:51.263Z