# Markov bases of binary graph models of K 4-minor free graphs - Mathematics > Combinatorics

Abstract: Markov width of a graph is a graph invariant defined as the maximum degree ofa Markov basis element for the corresponding graph model for binary contingencytables. We show that a graph has Markov width at most four if and only if itcontains no $K 4$ as a minor, answering a question of Develin and Sullivant. Wealso present a lower bound of order $\Omegan^{2-\varepsilon}$ on the Markovwidth of $K n$.

Author: Daniel Král', Serguei Norine, Ondrej Pangrác

Source: https://arxiv.org/