一类可图拟阵的二阶圈图的哈密顿性  

Hamiltonian Properties of Second-order Circuit Graphs of a Class of Graphic Matroid

作　　者：李亚宁 刘彬 邓梓健 王丽煊 火博丰 尹君 LI Ya-ning;LIU Bin;DENG Zi-jian;WANG Li-xuan;HUO Bo-feng;YIN Jun(College of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China;Key Laboratory of the Internet of Things of Qinghai Province,Xining 810008,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008 [2]青海省物联网重点实验室,青海西宁810008

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第5期540-544,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11961055,11801296)。

摘　　要：为研究一般连通拟阵的二阶圈图的哈密顿性,选取完全二部图K_(2,n)和K_(3,n)进行讨论,证明这两类圈拟阵的二阶圈图的哈密顿性,并证明K_(2,n)的圈拟阵的二阶圈图的连通度和泛圈性,对K_(2,n),K_(3,n)的圈拟阵的二阶圈图的一致哈密顿性提出了一个猜想。The Hamiltonian properties of the second-order circuit graphs of general connected matroids are studied in the paper. The complete bipartite graphs K_(2,n) and K_(3,n) are selected for discussion to prove the Hamiltonian property of the second-order circuit graphs of the two kinds of circuit matroids and the connectivity and pancyclic property of the second-order circuit graphs of the circuit matroids of K_(2,n). Also,a conjecture on the consistent Hamiltonian property of the second-order circuit graphs of the circuit matroids of K_(2,n) and K_(3,n) is proposed in the paper.

关 键 词：连通拟阵 完全二部图 二阶圈图 哈密顿性 

分 类 号：O157.5[理学—数学]