English

The Alon-Tarsi Number of A Toroidal Grid

Combinatorics 2020-01-01 v1

Abstract

The Alon-Tarsi number AT(G)AT(G) of a graph GG is the smallest kk for which there is an orientation DD of GG with max indegree k1k-1 such that the number of even and odd circulations contained in D are different. In this paper, we show that the Alon--Tarsi number of toroidal grids Tm,n=CmCnT_{m,n}=C_m\Box C_n equals 44 when m,nm,n are both odd and 33 otherwise.

Keywords

Cite

@article{arxiv.1912.12466,
  title  = {The Alon-Tarsi Number of A Toroidal Grid},
  author = {Zhiguo Li and Zeling Shao and Fedor Petrov and Alexey Gordeev},
  journal= {arXiv preprint arXiv:1912.12466},
  year   = {2020}
}