A survey on Hamilton cycles in directed graphs

被引：43
|
作者：
Kuehn, Daniela [1 ]
Osthus, Deryk [1 ]
机构：
[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2012年 / 33卷 / 05期
关键词：
SUFFICIENT CONDITIONS; PATHS; DIGRAPH; TOURNAMENTS; CONJECTURE; CIRCUITS; NUMBER; PROOF;
D O I：
10.1016/j.ejc.2011.09.030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We survey some recent results on long-standing conjectures regarding Hamilton cycles in directed graphs, oriented graphs and tournaments. We also combine some of these to prove the following approximate result towards Kelly's conjecture on Hamilton decompositions of regular tournaments: the edges of every regular tournament can be covered by a set of Hamilton cycles which are 'almost' edge-disjoint. We also highlight the role that the notion of 'robust expansion' plays in several of the proofs. New and old open problems are discussed. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：750 / 766
页数：17
相关论文
共 50 条
  • [41] HAMILTON CYCLES IN BIDIRECTED COMPLETE GRAPHS
    Busch, Arthur
    Mutar, Mohammed A.
    Slilaty, Daniel
    CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2022, 17 (02) : 137 - 149
  • [42] On Covering Expander Graphs by Hamilton Cycles
    Glebov, Roman
    Krivelevich, Michael
    Szabo, Tibor
    RANDOM STRUCTURES & ALGORITHMS, 2014, 44 (02) : 183 - 200
  • [43] Rainbow hamilton cycles in random graphs
    Frieze, Alan
    Loh, Po-Shen
    RANDOM STRUCTURES & ALGORITHMS, 2014, 44 (03) : 328 - 354
  • [44] Hamilton cycles in random lifts of graphs
    Burgin, K.
    Chebolu, P.
    Cooper, C.
    Frieze, A. M.
    EUROPEAN JOURNAL OF COMBINATORICS, 2006, 27 (08) : 1282 - 1293
  • [45] Compatible Hamilton cycles in Dirac graphs
    Michael Krivelevich
    Choongbum Lee
    Benny Sudakov
    Combinatorica, 2017, 37 : 697 - 732
  • [46] PANCYCLIC HAMILTON CYCLES IN RANDOM GRAPHS
    COOPER, C
    DISCRETE MATHEMATICS, 1991, 91 (02) : 141 - 148
  • [47] Hamilton cycles in infinite cubic graphs
    Pitz, Max F.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (03):
  • [48] On Hamilton cycles in certain planar graphs
    Sanders, DP
    JOURNAL OF GRAPH THEORY, 1996, 21 (01) : 43 - 50
  • [49] Disjoint Hamilton cycles in transposition graphs
    Hussak, Walter
    DISCRETE APPLIED MATHEMATICS, 2016, 206 : 56 - 64
  • [50] Disjoint cycles in directed graphs
    Yan, Jin
    ARS COMBINATORIA, 2018, 136 : 21 - 27
12345