Variable Degeneracy of Planar Graphs without Chorded 6-Cycles  

作　　者：Hui Hui FANG Dan Jun HUANG Tao WANG Wei Fan WANG 

机构地区：[1]School of Mathematics and Statistics,He’nan University,Kaifeng,475004,P.R.China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,321004,P.R.China [3]Center for Applied Mathematics,He’nan University,Kaifeng,475004,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第11期2735-2750,共16页数学学报（英文版）

基　　金：supported by NSFC(Grant Nos.12171436 and 12371360);supported by NSFC(Grant No.12031018);NSFSD(Grant No.ZR2022MA060)。

摘　　要：A cover of a graph G is a graph H with vertex set V(H)=∪_(v∈V(G))L_(v),where L_(v)={v}×[s],and the edge set M=∪_(uv∈E(G))M_(uv),where Muv is a matching between L_(u) and L_(v).A vertex set T⊆V(H)is a transversal of H if∣T∩Lv∣=1 for each v∈V(G).Let f be a nonnegative integer valued function on the vertex-set of H.If for any nonempty subgraphΓof H[T],there exists a vertex x∈V(H)such that d(x)<f(x),then T is called a strictly f-degenerate transversal.In this paper,we give a sufficient condition for the existence of strictly f-degenerate transversal for planar graphs without chorded 6-cycles.As a consequence,every planar graph without subgraphs isomorphic to the configurations is DP-4-colorable.

关 键 词：Variable degeneracy DP-coloring list coloring planar graph 

分 类 号：O157.5[理学—数学]