The Alon-Tarsi number of a planar graph minus a matching

Jarosław Grytczuk , Xuding Zhu

Abstract

This paper proves that every planar graph Gcontains a matching M such that the Alon-Tarsi number of G −M is at most 4. As a consequence, G −M is 4-paintable, and hence G itself is 1-defective 4-paintable. This improves a result of Cushing and Kierstead (2010) [5], who proved that every planar graph is 1-defective 4-choosable