English

Locally self-avoiding eulerian tours

Combinatorics 2017-01-17 v2

Abstract

It was independently conjectured by H\"aggkvist in 1989 and Kriesell in 2011 that given a positive integer \ell, every simple eulerian graph with high minimum degree (depending on \ell) admits an eulerian tour such that every segment of length at most \ell of the tour is a path. Bensmail, Harutyunyan, Le and Thomass\'e recently verified the conjecture for 4-edge-connected eulerian graphs. Building on that proof, we prove here the full statement of the conjecture. This implies a variant of the path case of Bar\'at-Thomassen conjecture that any simple eulerian graph with high minimum degree can be decomposed into paths of fixed length and possibly an additional shorter path.

Keywords

Cite

@article{arxiv.1611.07486,
  title  = {Locally self-avoiding eulerian tours},
  author = {Tien-Nam Le},
  journal= {arXiv preprint arXiv:1611.07486},
  year   = {2017}
}

Comments

14 pages, no figure

R2 v1 2026-06-22T17:01:21.224Z