不含4-圈和7-圈环面图(F,F3)-分解的存在性  

The Existence of(F,F3)-partition for Toroidal Graphs Without 4-and 7-cycles

作　　者：陈敏 朱嫒娜 王艺桥[2] CHEN Min;ZHU Aina;WANG Yiqiao(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;School of Management,Beijing University of Chinese Medicine,Beijing,100029,P.R.China)

机构地区：[1]浙江师范大学数学与计算机科学学院,金华浙江321004 [2]北京中医药大学管理学院,北京100029

出　　处：《数学进展》2022年第6期979-988,共10页Advances in Mathematics（China）

基　　金：国家自然科学基金(Nos.11971437,12071048);浙江省自然科学基金(No.LY19A010015)。

摘　　要：令G=(V,E)是一个图.图G的(F,F_(d))-分解是指将G的顶点集合V(G)分解为2个子集V_(1)和V_(2),使得子图G[V_(1)]是森林,G[V_(2)]是最大度至多为d的森林.本文证明了每个不含4-圈和7-圈的环面图有(F,F_(3))-分解.Let G=(V,E)be a graph.An(F,F_(d))-partition of a graph G is to divide the vertex set V(G)into two sets V_(1) and V_(2) such that G[V_(1)] is a forest and G[V_(2)] is the forest with bounded maximum degree at most d.In this paper,we prove that every toroidal graph without 4-cycles and 7-cycles admits an(F,F_(3))-partition.

关 键 词：环面图 森林分解 权转移 圈 

分 类 号：O157.5[理学—数学]