List Edge Colorings of Planar Graphs without Non-induced 7-cycles  

作　　者：Li Zhang Hajo Broersma You Lu Shenggui Zhang 

机构地区：[1]School of Mathematics and Computer Science,Yan’an University,Yan’an,716000,P.R.China [2]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an,710129,P.R.China [3]Faculty of Electrical Engineering,Mathematics and Computer Science,University of Twente,P.O.Box 217,7500 AE,Enschede,Netherlands [4]Xi’an-Budapest Joint Research Center for Combinatorics,Northwestern Polytechnical University,Xi’an,710129,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第3期1037-1054,共18页数学学报(英文版)

基　　金：Supported by NSFC(Grant Nos.12271438,12071370 and U1803263);China Scholarship Council(Grant No.202006290386)。

摘　　要：A graph G is edge-k-choosable if,for any assignment of lists L(e)of at least k colors to all edges e∈E(G),there exists a proper edge coloring such that the color of e belongs to L(e)for all e∈E(G).One of Vizing’s classic conjectures asserts that every graph is edge-(Δ+1)-choosable.It is known since 1999 that this conjecture is true for general graphs withΔ≤4.More recently,in 2015,Bonamy confirmed the conjecture for planar graph withΔ≥8,but the conjecture is still open for planar graphs with 5≤Δ≤7.We confirm the conjecture for planar graphs withΔ≥6 in which every 7-cycle(if any)induces a C_(7)(so,without chords),thereby extending a result due to Dong,Liu and Li.

关 键 词：Planar graph list edge coloring edge-k-choosability Combinatorial Nullstellensatz DISCHARGING 

分 类 号：O157.5[理学—数学]