### Abstract

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

Original language | English |
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Pages (from-to) | 167-176 |

Number of pages | 10 |

Journal | Journal of Graph Theory |

Volume | 29 |

Issue number | 3 |

Publication status | Published - Nov 1998 |

### Fingerprint

### Keywords

- Hamilton cycle
- Regularity lemma

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*29*(3), 167-176.

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

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 29, no. 3, pp. 167-176.

}

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 -