不含4-圈和三角化6-圈的环面图森林分解  

A forest partition of toroidal graphs with neither 4-cycles nor triangular 6-cycles

作　　者：李玲静 陈敏[1] LI Lingjing;CHEN Min(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学科学学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2024年第4期391-397,共7页Journal of Zhejiang Normal University:Natural Sciences

基　　金：浙江省自然科学基金重点资助项目(LZ23A010004);国家自然科学基金资助项目(12371360)。

摘　　要：假设G是一个有限简单图.令V(G)和E(G)分别表示图G的点集合和边集合.若能将G的点集合V(G)划分为2个不交的子集合V_(1)和V_(2),使得由V_(1)和V_(2)导出的子图满足G[V_(1)]是森林且G[V_(2)]是最大度至多为d的森林,则称G有一个(F,F_(d))-分解.运用反证法,通过对极小反例的结构分析,找到可约构形,再通过权转移讨论证明:不含4-圈和三角化6-圈的环面图有(F,F_(3))-分解.It was studied a finite simple graph G with vertex set V(G)and edge set E(G).An(F,F_(d))-parti-tion was introduced for G while V(G)could be divided into two disjoint subsets V_(1)and V_(2)such that G[V_(1)]constructed a forest and G[V_(2)]also constructed a forest with maximum degree at most d.Based on the method of proof by contradiction,some useful reducible configurations were obtained by analyzing the structure of min-imal counterexamples,and then argued by an appropriate discharging method.It was finally proved that every toroidal graph with neither 4-cycles and triangular 6-cycles admitted an(F,F_(3))-partition.

关 键 词：环面图 三角化 森林分解 最大度 权转移 

分 类 号：O157.5[理学—数学]