Packing Hamilton Cycles Online

Joseph Briggs; Alan Frieze; Michael Krivelevich; Po Shen Loh; Benny Sudakov

doi:10.1017/S0963548318000159

Packing Hamilton Cycles Online

Joseph Briggs, Alan Frieze, Michael Krivelevich, Po Shen Loh, Benny Sudakov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

It is known that w.h.p. the hitting time τ_2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of K_n are presented one by one then w.h.p. it is possible to colour the edges online with σ colours so that at time τ_2σ each colour class is Hamiltonian.

Original language	English
Pages (from-to)	475-495
Number of pages	21
Journal	Combinatorics Probability and Computing
Volume	27
Issue number	4
DOIs	https://doi.org/10.1017/S0963548318000159
State	Published - 1 Jul 2018

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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title = "Packing Hamilton Cycles Online",

abstract = "It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to colour the edges online with σ colours so that at time τ2σ each colour class is Hamiltonian.",

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AU - Frieze, Alan

AU - Krivelevich, Michael

AU - Loh, Po Shen

AU - Sudakov, Benny

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Y1 - 2018/7/1

N2 - It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to colour the edges online with σ colours so that at time τ2σ each colour class is Hamiltonian.

AB - It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to colour the edges online with σ colours so that at time τ2σ each colour class is Hamiltonian.

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DO - 10.1017/S0963548318000159

M3 - مقالة

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EP - 495

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 4

ER -

Packing Hamilton Cycles Online

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All Science Journal Classification (ASJC) codes

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