无4-圈的IC-可平面图的线性2-荫度  

The Linear 2-Arboricity of 4-Cycle Free IC-Planar Graphs

作　　者：闫清华 向长媛 徐常青[1] Yan Qinghua;Xiang Changyuan;Xu Changqing(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《南开大学学报(自然科学版)》2023年第5期64-76,共13页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(12071260,12001154)。

摘　　要：设G是最大度为Δ的IC-可平面图.图G的线性k-边染色是指G的一个映射φ:E(G)→{1,2,···,k}满足由染同一种颜色的边集导出的子图的连通分支均是长至多为2的路.图G的线性2-荫度是使G有一个线性k-边染色的最小正整数k.运用权转移方法研究了IC-可平面图的线性2-荫度,得到无4-圈的IC-可平面图的线性2-荫度的上界为[△+1/2]+3.Let G be an IC-planar graph with maximum degree Z.The linear k-edge coloring of G is a mapping:φ:E(G)→{1,2,···,k},such that the set of edges having the same color induces a subgraph whose components are paths of length at most 2.The linear 2-arboricity of a graph G is the smallest k such that G has a linear k-edge coloring.The linear 2-arboricity of IC-planar graph G is discussed by discharging method,and it's obtained that[△+1/2]+3 is an upper bound for the linear 2-arboricity of 4-2 cycle free IC-planar graph G.

关 键 词：IC-可平面图 线性2-荫度 权转移方法 

分 类 号：O212.8[理学—概率论与数理统计]