COLORFUL HAMILTON CYCLES IN RANDOM GRAPHS

被引：1
|
作者：
Chakraborti, Debsoumya [1 ]
Frieze, Alan M. [2 ]
Hasabnis, Mihir [2 ]
机构：
[1] Inst Basic Sci IBS, Discrete Math Grp, Daejeon 34126, South Korea
[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
来源：
SIAM JOURNAL ON DISCRETE MATHEMATICS | 2023年 / 37卷 / 01期
关键词：
random graph; rainbow Hamilton cycle; path rotation-extention technique;
D O I：
10.1137/21M1403291
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given an n vertex graph whose edges have colored from one of r colors C = {c1, c2, . . . , cr}, we define the Hamilton cycle color profile hcp(G) to be the set of vectors (m1, m2, ... , mr) \in [0, n]r such that there exists a Hamilton cycle that is the concatenation of r paths P1, P2, . . . , Pr, where Pi contains mi edges of color ci. We study hcp(Gn,p) when the edges are randomly colored. We discuss the profile close to the threshold for the existence of a Hamilton cycle and the threshold for when hcp(Gn,p) = {(m1, m2, . . . , mr) \in [0, n]r : m1 + m2 + \cdot \cdot \cdot + mr = n}.
引用
收藏
页码：51 / 64
页数：14
相关论文
共 50 条
  • [1] Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs
    Nenadov, Rajko
    Skoric, Nemanja
    RANDOM STRUCTURES & ALGORITHMS, 2019, 54 (01) : 187 - 208
  • [2] Hamilton cycles in random graphs and directed graphs
    Cooper, C
    Frieze, A
    RANDOM STRUCTURES & ALGORITHMS, 2000, 16 (04) : 369 - 401
  • [3] HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS
    Balogh, Jozsef
    Bollobas, Bela
    Krivelevich, Michael
    Muller, Tobias
    Walters, Mark
    ANNALS OF APPLIED PROBABILITY, 2011, 21 (03): : 1053 - 1072
  • [4] ON MATCHINGS AND HAMILTON CYCLES IN RANDOM GRAPHS
    FRIEZE, AM
    SURVEYS IN COMBINATORICS, 1989, 1989, 141 : 84 - 114
  • [5] Compatible Hamilton Cycles in Random Graphs
    Krivelevich, Michael
    Lee, Choongbum
    Sudakov, Benny
    RANDOM STRUCTURES & ALGORITHMS, 2016, 49 (03) : 533 - 557
  • [6] Rainbow hamilton cycles in random graphs
    Frieze, Alan
    Loh, Po-Shen
    RANDOM STRUCTURES & ALGORITHMS, 2014, 44 (03) : 328 - 354
  • [7] 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
  • [8] PANCYCLIC HAMILTON CYCLES IN RANDOM GRAPHS
    COOPER, C
    DISCRETE MATHEMATICS, 1991, 91 (02) : 141 - 148
  • [9] Hamilton cycles in random lifts of graphs
    Luczak, Tomasz
    Witkowski, Lukasz
    Witkowski, Marcin
    EUROPEAN JOURNAL OF COMBINATORICS, 2015, 49 : 105 - 116
  • [10] Hamilton cycles in random lifts of directed graphs
    Chebolu, Prasad
    Frieze, Alan
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2008, 22 (02) : 520 - 540
12345