2022/07/20 by Xu, Rongxing, Zhu, Xuding
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2207.09659
A decomposition of a graph G is a family of subgraphs of G whose edge sets form a partition of E(G). In this paper, we prove that every triangle-free planar graph G can be decomposed into a 2-degenerate graph and a matching. Consequently, every triangle-free planar graph G has a matching M such that G-M is online 3-DP-colorable. This strengthens an earlier result in [R. Škrekovski, \em A Grötzsch-Type Theorem for List Colourings with Impropriety One, Combin. Prob. Comput. 8 (1999), 493-507] that every triangle-free planar graph is 1-defective 3-choosable.