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arXiv · 1611.07486

Locally self-avoiding eulerian tours

Tien-Nam Le
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Abstract

It was independently conjectured by Häggkvist 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 Thomassé 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 Barát-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.

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Tien-Nam Le. 2017-01-15. Locally self-avoiding eulerian tours. https://arxiv.org/abs/1611.07486

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