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 , every simple eulerian graph with high minimum degree (depending on ) admits an eulerian tour such that every segment of length at most 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