A note on Hamiltonian cycles in planar graphs

被引：0
|
作者：
Kreh, Martin [1 ]
机构：
[1] Univ Hildesheim, Inst Math & Appl Comp Sci, Samelson pl 1, D-31141 Hildesheim, Germany
来源：
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2023年 / 15卷 / 01期
关键词：
Hamiltonian cycle; planar graph; Diophantine equation;
D O I：
10.1142/S1793830922500604
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Unlike the problem of finding Eulerian cycles, the problem of deciding whether a given graph has a Hamiltonian cycle is NP-complete, even when restricting to planar graphs. There are however some criteria that. can be used in special cases. One of them can be derived by Grinberg's theorem. In this note, we give some more (slightly more general) criteria derived from Grinberg's theorem to show that a graph does not have a Hamiltonian cycle.
引用
收藏
页数：5
相关论文
共 50 条
  • [41] Hamiltonian cycles in solid grid graphs
    Umans, C
    Lenhart, W
    38TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, 1997, : 496 - 505
  • [42] NUMBER OF HAMILTONIAN CYCLES IN PLANAR TRIANGULATIONS
    Liu, Xiaonan
    Yu, Xingxing
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2021, 35 (02) : 1005 - 1021
  • [43] On Finding Hamiltonian Cycles in Barnette Graphs
    Bagheri, Behrooz Gh
    Fleischner, Herbert
    Feder, Tomas
    Subi, Carlos
    FUNDAMENTA INFORMATICAE, 2022, 188 (01) : 1 - 14
  • [44] HAMILTONIAN CYCLES IN RANDOM REGULAR GRAPHS
    FENNER, TI
    FRIEZE, AM
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 1984, 37 (02) : 103 - 112
  • [45] Cycles of many lengths in Hamiltonian graphs
    Bucic, Matija
    Gishboliner, Lior
    Sudakov, Benny
    FORUM OF MATHEMATICS SIGMA, 2022, 10
  • [46] Powers of Hamiltonian cycles in multipartite graphs
    DeBiasio, Louis
    Martin, Ryan R.
    Molla, Theodore
    DISCRETE MATHEMATICS, 2022, 345 (04)
  • [47] Hamiltonian Cycles in T-Graphs
    J. R. Reay
    T. Zamfirescu
    Discrete & Computational Geometry, 2000, 24 : 497 - 502
  • [48] Finding Large Cycles in Hamiltonian Graphs
    Feder, Tomas
    Motwani, Rajeev
    PROCEEDINGS OF THE SIXTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2005, : 166 - 175
  • [49] HAMILTONIAN CYCLES IN CAYLEY COLOR GRAPHS
    KLERLEIN, JB
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (07): : A654 - A654
  • [50] Hamiltonian Cycles in Normal Cayley Graphs
    Jose Montellano-Ballesteros, Juan
    Santiago Arguello, Anahy
    GRAPHS AND COMBINATORICS, 2019, 35 (06) : 1707 - 1714
12345