A remark on Hamilton cycles with few colors

Igor Balla; Alexey Pokrovskiy; Benny Sudakov

A remark on Hamilton cycles with few colors

Igor Balla, Alexey Pokrovskiy, Benny Sudakov

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

Abstract

Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge-coloring of K_n with n colors contains a Hamilton cycle with ≤ O(log n) colors. They proved that there is always a Hamilton cycle with ≤ 8^pn colors. In this note we improve this bound to O(log³ n).

Original language	English
Pages (from-to)	73-77
Number of pages	5
Journal	Moscow Journal of Combinatorics and Number Theory
Volume	7
Issue number	3
State	Published - 2017
Externally published	Yes

Keywords

Hamilton cycle
probabilistic methods
spectral techniques

Cite this

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title = "A remark on Hamilton cycles with few colors",

abstract = "Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge-coloring of Kn with n colors contains a Hamilton cycle with ≤ O(log n) colors. They proved that there is always a Hamilton cycle with ≤ 8pn colors. In this note we improve this bound to O(log3 n).",

keywords = "Hamilton cycle, probabilistic methods, spectral techniques",

author = "Igor Balla and Alexey Pokrovskiy and Benny Sudakov",

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AU - Sudakov, Benny

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AB - Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge-coloring of Kn with n colors contains a Hamilton cycle with ≤ O(log n) colors. They proved that there is always a Hamilton cycle with ≤ 8pn colors. In this note we improve this bound to O(log3 n).

KW - Hamilton cycle

KW - probabilistic methods

KW - spectral techniques

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JO - Moscow Journal of Combinatorics and Number Theory

JF - Moscow Journal of Combinatorics and Number Theory

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A remark on Hamilton cycles with few colors

Abstract

Keywords

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