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}.
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页码：51 / 64
页数：14
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