Contractible Edges and Longest Cycles in 3-Connected Graphs

被引：0
|
作者：
Egawa, Yoshimi [1 ]
Nakamura, Shunsuke [2 ]
机构：
[1] Tokyo Univ Sci, Dept Appl Math, 1-3 Kagurazaka,Shinju Ku, Tokyo 1628601, Japan
[2] Natl Inst Technol, Kurume Coll, Dept Liberal Arts Sci & Math, 1-1-1 Komorino, Fukuoka 8308555, Japan
来源：
GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 01期
关键词：
3-Connected graph; Contractible edge; Longest cycle; MAXIMUM NUMBER;
D O I：
10.1007/s00373-022-02609-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that if G is a 3-connected graph of order at least 5, then there exists a longest cycle C of G such that the number of contractible edges of G which are on C is greater than or equal to (|E(C)| + 5) /6.
引用
收藏
页数：16
相关论文
共 50 条
  • [21] Contractible Non-edges in 3-Connected Infinite Graphs
    Chan, Tsz Lung
    GRAPHS AND COMBINATORICS, 2019, 35 (06) : 1447 - 1458
  • [22] Contractible Non-edges in 3-Connected Infinite Graphs
    Tsz Lung Chan
    Graphs and Combinatorics, 2019, 35 : 1447 - 1458
  • [23] Longest cycles in 3-connected hypergraphs and bipartite graphs
    Kostochka, Alexandr
    Lavrov, Mikhail
    Luo, Ruth
    Zirlin, Dara
    Journal of Graph Theory, 2022, 99 (04): : 758 - 782
  • [24] Contractible Edges and Contractible Triangles in a 3-Connected Graph
    Ando, Kiyoshi
    Egawa, Yoshimi
    GRAPHS AND COMBINATORICS, 2021, 37 (05) : 1807 - 1821
  • [25] Longest cycles in 3-connected hypergraphs and bipartite graphs
    Kostochka, Alexandr
    Lavrov, Mikhail
    Luo, Ruth
    Zirlin, Dara
    JOURNAL OF GRAPH THEORY, 2022, 99 (04) : 758 - 782
  • [26] Contractible Edges and Contractible Triangles in a 3-Connected Graph
    Kiyoshi Ando
    Yoshimi Egawa
    Graphs and Combinatorics, 2021, 37 : 1807 - 1821
  • [27] Maximum Number of Contractible Edges on Hamiltonian Cycles of a 3-Connected Graph
    Kyo Fujita
    Graphs and Combinatorics, 2002, 18 : 447 - 478
  • [28] Maximum number of contractible edges on Hamiltonian cycles of a 3-connected graph
    Fujita, K
    GRAPHS AND COMBINATORICS, 2002, 18 (03) : 447 - 478
  • [29] An included-minor result for 3-connected graphs with contractible edges
    Turner, GE
    DISCRETE MATHEMATICS, 2000, 214 (1-3) : 291 - 297
  • [30] LONGEST CYCLES IN 3-CONNECTED 3-REGULAR GRAPHS
    BONDY, JA
    SIMONOVITS, M
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1980, 32 (04): : 987 - 992
12345