Hamiltonicity of cubic Cayley graphs

被引:0
|
作者
Glover, Henry [1 ]
Marusic, Dragan [2 ,3 ]
机构
[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA
[2] Univ Ljubljana, Ljubljana 1000, Slovenia
[3] Univ Ljubljana, IMFM, Koper, Slovenia
关键词
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Following a problem posed by Lovasz in 1969, it is believed that every finite connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from finite groups having a (2, s, 3)-presentation, that is, for groups G = < a, b vertical bar a(2) = 1, b(s) = 1, ( ab)(3) = 1, ...> generated by an involution a and an element b of order s >= 3 such that their product ab has order 3. More precisely, it is shown that the Cayley graph X = Cay(G, {a, b, b(-1)}) has a Hamilton cycle when vertical bar G vertical bar (and thus s) is congruent to 2 modulo 4, and has a long cycle missing only two adjacent vertices (and thus necessarily a Hamilton path) when vertical bar G vertical bar is congruent to 0 modulo 4.
引用
收藏
页码:775 / 787
页数:13
相关论文
共 50 条
  • [11] Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes
    Kardos, Frantisek
    SIAM REVIEW, 2022, 64 (02) : 425 - 465
  • [12] Enumeration of cubic Cayley graphs on dihedral groups
    Xue Yi Huang
    Qiong Xiang Huang
    Lu Lu
    Acta Mathematica Sinica, English Series, 2017, 33 : 996 - 1010
  • [13] The solution of a problem of Godsil on cubic Cayley graphs
    Li, CH
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 1998, 72 (01) : 140 - 142
  • [14] Enumeration of Cubic Cayley Graphs on Dihedral Groups
    Xue Yi HUANG
    Qiong Xiang HUANG
    Lu LU
    Acta Mathematica Sinica,English Series, 2017, (07) : 996 - 1010
  • [15] The planar cubic Cayley graphs of connectivity 2
    Georgakopoulos, Agelos
    EUROPEAN JOURNAL OF COMBINATORICS, 2017, 64 : 152 - 169
  • [16] Enumeration of Cubic Cayley Graphs on Dihedral Groups
    Xue Yi HUANG
    Qiong Xiang HUANG
    Lu LU
    ActaMathematicaSinica, 2017, 33 (07) : 996 - 1010
  • [17] Enumeration of Cubic Cayley Graphs on Dihedral Groups
    Huang, Xue Yi
    Huang, Qiong Xiang
    Lu, Lu
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2017, 33 (07) : 996 - 1010
  • [18] On cubic Cayley graphs of finite simple groups
    Fang, XG
    Li, CH
    Wang, J
    Xu, MY
    DISCRETE MATHEMATICS, 2002, 244 (1-3) : 67 - 75
  • [19] Cubic (m,n)-metacirculant graphs which are not Cayley graphs
    Tan, ND
    DISCRETE MATHEMATICS, 1996, 154 (1-3) : 237 - 244
  • [20] A new heuristic for detecting non-Hamiltonicity in cubic graphs
    Filar, Jerzy A.
    Haythorpe, Michael
    Rossomakhine, Serguei
    COMPUTERS & OPERATIONS RESEARCH, 2015, 64 : 283 - 292