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COLORFUL HAMILTON CYCLES IN RANDOM GRAPHS

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Title
COLORFUL HAMILTON CYCLES IN RANDOM GRAPHS
Author(s)
Debsoumya Chakraborti; Frieze, A.M.; Hasabnis, M.
Publication Date
2023-03
Journal
SIAM Journal on Discrete Mathematics, v.37, no.1, pp.51 - 64
Publisher
Society for Industrial and Applied Mathematics Publications
Abstract
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 +... + mr = n}. © 2023 Society for Industrial and Applied Mathematics.
URI
https://pr.ibs.re.kr/handle/8788114/13192
DOI
10.1137/21M1403291
ISSN
0895-4801
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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