一类具有强偶圈分解的4-正则线图  

A Class of 4-Regular Line Graphs with Strong Even Cycle Decomposition

作　　者：王丹丹 WANG Dan-dan(School of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学理学院数学系,南京211106

出　　处：《西安文理学院学报（自然科学版）》2022年第2期5-10,52,共7页Journal of Xi’an University(Natural Science Edition)

摘　　要：如果一个图的边集能划分成偶数长度圈的集合,则称该图有一个偶圈分解.如果一个图的任何一个具有偶数条边的细分,都有一个偶圈分解,则称该图是强偶圈分解的.在文献[European Journal of Combinatorics,94(2021),103315]中已证明:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个线性森林(即这个森林仅仅由路组成),则L(G)是强偶圈分解的.本文推广上述结论,证明了如下定理:对于2-连通立方图G,如果它存在一个圈C使得G-V(C)是一个森林,则L(G)是强偶圈分解的.If the edge set of a graph can be divided into a set of cycles with even length,the graph is said to have an even cycle decomposition.If any subdivision of a graph with even edges has an even cycle decomposition,we call the graph a strong even cycle decomposition.The following conclusions have been proved in the literature[European Journal of combinatorics,94(2021),103315].That is,for 2-connected cubic graph G,if it has a cycle C so that G-V(C)is a linear forest(that is,the forest is only composed of paths),then L(G)is strongly even cycle decomposition.In this paper,we generalize the above conclusion and prove the following theorem:for 2-connected cubic graph G,if it has a cycle C so that G-V(C)is a forest,then L(G)is strongly even cycle decomposition.

关 键 词：偶圈分解 强偶圈分解 立方图 线图 

分 类 号：O175.5[理学—数学]