Avoiding 7-circuits in 2-factors of cubic graphs

被引：0
|
作者：
Lukotka, Robert [1 ]
机构：
[1] Trnava Univ, Fac Educ, Dept Math & Comp Sci, Trnava, Slovakia
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2014年 / 21卷 / 04期
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：
Let G be a cyclically 4-edge-connected cubic graph with girth at least 7 on n vertices. We show that G has a 2-factor F such that at least a linear amount of vertices is not in 7-circuits of F. More precisely, there are at least n/657 vertices of G that are not in 7-circuits of F. If G is cyclically 6-edge-connected then the bound can be improved to n/189. As a corollary we obtain bounds on the oddness and on the length of the shortest travelling salesman tour in a cyclically 4-edge-connected (6-edge-connected) cubic graph of girth at least 7.
引用
收藏
页数：12
相关论文
共 50 条
  • [31] Cycles in 2-Factors of Balanced Bipartite Graphs
    Guantao Chen
    Ralph J. Faudree
    Ronald J. Gould
    Michael S. Jacobson
    Linda Lesniak
    Graphs and Combinatorics, 2000, 16 : 67 - 80
  • [32] ON 2-FACTORS WITH A SPECIFIED NUMBER OF COMPONENTS IN LINE GRAPHS
    Chiba, S.
    Egawa, Y.
    Fujisawa, J.
    Saito, A.
    Schiermeyer, I.
    Tsugaki, M.
    Yamashita, T.
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2019, 88 (03): : 541 - 546
  • [33] On 2-factors containing 1-factors in bipartite graphs
    Chen, Guantao
    Gould, Ronald J.
    Jacobson, Michael S.
    Discrete Mathematics, 1999, 197-198 : 185 - 194
  • [34] On 2-factors containing 1-factors in bipartite graphs
    Chen, GT
    Gould, RJ
    Jacobson, MS
    DISCRETE MATHEMATICS, 1999, 197 (1-3) : 185 - 194
  • [35] Circumferences of 2-factors in claw-free graphs
    Cada, Roman
    Chiba, Shuya
    DISCRETE MATHEMATICS, 2013, 313 (19) : 1934 - 1943
  • [36] Regular bipartite graphs with all 2-factors isomorphic
    Aldred, REL
    Funk, M
    Jackson, B
    Labbate, D
    Sheehan, J
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2004, 92 (01) : 151 - 161
  • [37] A Generalization of a result of Catlin: 2-factors in line graphs
    Gould, Ronald J.
    Hynds, Emily A.
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2018, 72 : 164 - 184
  • [38] 2-factors with the bounded number of components in line graphs
    Xiong, Liming
    APPLIED MATHEMATICS LETTERS, 2011, 24 (05) : 731 - 734
  • [39] Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture
    Bagheri, Behrooz Gh
    Feder, Tomas
    Fleischner, Herbert
    Subi, Carlos
    JOURNAL OF GRAPH THEORY, 2021, 96 (02) : 269 - 288
  • [40] 2-FACTORS OF BIPARTITE GRAPHS WITH ASYMMETRIC MINIMUM DEGREES
    Czygrinow, Andrzej
    Debiasio, Louis
    Kierstead, H. A.
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2010, 24 (02) : 486 - 504
12345