A Proof of the Bar\'at-Thomassen Conjecture

Julien Bensmail; Ararat Harutyunyan; Tien-Nam Le; Martin Merker; Stéphan Thomassé

A Proof of the Bar\'at-Thomassen Conjecture

Combinatorics 2016-11-09 v2

Authors: Julien Bensmail , Ararat Harutyunyan , Tien-Nam Le , Martin Merker , Stéphan Thomassé

Abstract

The Bar\'at-Thomassen conjecture asserts that for every tree $T$ on $m$ edges, there exists a constant $k_T$ such that every $k_T$ -edge-connected graph with size divisible by $m$ can be edge-decomposed into copies of $T$ . So far this conjecture has only been verified when $T$ is a path or when $T$ has diameter at most 4. Here we prove the full statement of the conjecture.

Keywords

Barát-Thomassen conjecture tree edge-connected graph edge-decomposition graph theory combinatorial proof

Cite

@article{arxiv.1603.00197,
  title  = {A Proof of the Bar\'at-Thomassen Conjecture},
  author = {Julien Bensmail and Ararat Harutyunyan and Tien-Nam Le and Martin Merker and Stéphan Thomassé},
  journal= {arXiv preprint arXiv:1603.00197},
  year   = {2016}
}

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16 pages

A Proof of the Bar\'at-Thomassen Conjecture

Abstract

Keywords

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