On the Pósa-Seymour Conjecture

János Komlós, Gábor N. Sárközy, E. Szemerédi

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

Paul Seymour conjectured that any graph G of order n and minimum degree at least k/k+1 n contains the kth power of a Hamilton cycle. We prove the following approximate version. For any ∈ > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least (k/k+1 + ∈)n, then G contains the kth power of a Hamilton cycle.

Original languageEnglish
Pages (from-to)167-176
Number of pages10
JournalJournal of Graph Theory
Volume29
Issue number3
Publication statusPublished - Nov 1998

Fingerprint

Hamilton Cycle
Minimum Degree
Integer
Graph in graph theory

Keywords

  • Hamilton cycle
  • Regularity lemma

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Komlós, J., Sárközy, G. N., & Szemerédi, E. (1998). On the Pósa-Seymour Conjecture. Journal of Graph Theory, 29(3), 167-176.

On the Pósa-Seymour Conjecture. / Komlós, János; Sárközy, Gábor N.; Szemerédi, E.

In: Journal of Graph Theory, Vol. 29, No. 3, 11.1998, p. 167-176.

Research output: Contribution to journalArticle

Komlós, J, Sárközy, GN & Szemerédi, E 1998, 'On the Pósa-Seymour Conjecture', Journal of Graph Theory, vol. 29, no. 3, pp. 167-176.
Komlós J, Sárközy GN, Szemerédi E. On the Pósa-Seymour Conjecture. Journal of Graph Theory. 1998 Nov;29(3):167-176.
Komlós, János ; Sárközy, Gábor N. ; Szemerédi, E. / On the Pósa-Seymour Conjecture. In: Journal of Graph Theory. 1998 ; Vol. 29, No. 3. pp. 167-176.
@article{03e71a489906470ab687fc053bf5eb3d,
title = "On the P{\'o}sa-Seymour Conjecture",
abstract = "Paul Seymour conjectured that any graph G of order n and minimum degree at least k/k+1 n contains the kth power of a Hamilton cycle. We prove the following approximate version. For any ∈ > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least (k/k+1 + ∈)n, then G contains the kth power of a Hamilton cycle.",
keywords = "Hamilton cycle, Regularity lemma",
author = "J{\'a}nos Koml{\'o}s and S{\'a}rk{\"o}zy, {G{\'a}bor N.} and E. Szemer{\'e}di",
year = "1998",
month = "11",
language = "English",
volume = "29",
pages = "167--176",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "3",

}

TY - JOUR

T1 - On the Pósa-Seymour Conjecture

AU - Komlós, János

AU - Sárközy, Gábor N.

AU - Szemerédi, E.

PY - 1998/11

Y1 - 1998/11

N2 - Paul Seymour conjectured that any graph G of order n and minimum degree at least k/k+1 n contains the kth power of a Hamilton cycle. We prove the following approximate version. For any ∈ > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least (k/k+1 + ∈)n, then G contains the kth power of a Hamilton cycle.

AB - Paul Seymour conjectured that any graph G of order n and minimum degree at least k/k+1 n contains the kth power of a Hamilton cycle. We prove the following approximate version. For any ∈ > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least (k/k+1 + ∈)n, then G contains the kth power of a Hamilton cycle.

KW - Hamilton cycle

KW - Regularity lemma

UR - http://www.scopus.com/inward/record.url?scp=0347599330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347599330&partnerID=8YFLogxK

M3 - Article

VL - 29

SP - 167

EP - 176

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -