Hamilton completion and the path cover number of sparse random graphs

Yahav Alon; Michael Krivelevich

doi:10.1016/j.ejc.2024.103934

Hamilton completion and the path cover number of sparse random graphs

Yahav Alon, Michael Krivelevich

Tel Aviv University

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

Abstract

We prove that for every ɛ>0 there is c₀ such that if G∼G(n,c/n), c≥c₀, then with high probability G can be covered by at most [Formula presented] vertex disjoint paths, which is essentially tight. This is equivalent to showing that, with high probability, at most [Formula presented] edges can be added to G to create a Hamiltonian graph.

Original language	English
Article number	103934
Journal	European Journal of Combinatorics
Volume	118
DOIs	https://doi.org/10.1016/j.ejc.2024.103934
State	Published - May 2024

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2024.103934

Cite this

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title = "Hamilton completion and the path cover number of sparse random graphs",

abstract = "We prove that for every ɛ>0 there is c0 such that if G∼G(n,c/n), c≥c0, then with high probability G can be covered by at most [Formula presented] vertex disjoint paths, which is essentially tight. This is equivalent to showing that, with high probability, at most [Formula presented] edges can be added to G to create a Hamiltonian graph.",

author = "Yahav Alon and Michael Krivelevich",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Ltd",

year = "2024",

month = may,

doi = "10.1016/j.ejc.2024.103934",

language = "الإنجليزيّة",

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T1 - Hamilton completion and the path cover number of sparse random graphs

AU - Alon, Yahav

AU - Krivelevich, Michael

PY - 2024/5

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N2 - We prove that for every ɛ>0 there is c0 such that if G∼G(n,c/n), c≥c0, then with high probability G can be covered by at most [Formula presented] vertex disjoint paths, which is essentially tight. This is equivalent to showing that, with high probability, at most [Formula presented] edges can be added to G to create a Hamiltonian graph.

AB - We prove that for every ɛ>0 there is c0 such that if G∼G(n,c/n), c≥c0, then with high probability G can be covered by at most [Formula presented] vertex disjoint paths, which is essentially tight. This is equivalent to showing that, with high probability, at most [Formula presented] edges can be added to G to create a Hamiltonian graph.

UR - http://www.scopus.com/inward/record.url?scp=85185308204&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2024.103934

DO - 10.1016/j.ejc.2024.103934

M3 - مقالة

SN - 0195-6698

VL - 118

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

M1 - 103934

ER -

Hamilton completion and the path cover number of sparse random graphs

Abstract

All Science Journal Classification (ASJC) codes

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