Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

Allan Lo; Vincent Pfenninger

Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

Allan Lo, Vincent Pfenninger

Mathematics

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

Abstract

A k-uniform tight cycle is a k-graph with a cyclic order of its vertices such that every k consecutive vertices from an edge. We show that for k≥3, every red-blue edge-coloured complete k-graph on n vertices contains k vertex-disjoint monochromatic tight cycles that together cover n−o(n) vertices.

Original language	English
Journal	Innovations in Graph Theory
Publication status	Accepted/In press - 8 May 2024

Bibliographical note

Not yet published as of 09/05/2024.

1 Finished
2 Active

Ramsey theory: an extremal perspective
Treglown, A. & Lo, A.
Engineering & Physical Science Research Council
1/01/22 → 31/12/24
Project: Research Councils
H2020_ERC_EXTCOMB
Osthus, D. & Kuhn, D.
European Commission
1/01/19 → 30/06/24
Project: EU
Matchings and tilings in graphs
Lo, A. & Treglown, A.
Engineering & Physical Science Research Council
1/03/21 → 29/02/24
Project: Research Councils

Cite this

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title = "Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles",

abstract = "A k-uniform tight cycle is a k-graph with a cyclic order of its vertices such that every k consecutive vertices from an edge. We show that for k≥3, every red-blue edge-coloured complete k-graph on n vertices contains k vertex-disjoint monochromatic tight cycles that together cover n−o(n) vertices.",

author = "Allan Lo and Vincent Pfenninger",

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AU - Pfenninger, Vincent

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PY - 2024/5/8

Y1 - 2024/5/8

N2 - A k-uniform tight cycle is a k-graph with a cyclic order of its vertices such that every k consecutive vertices from an edge. We show that for k≥3, every red-blue edge-coloured complete k-graph on n vertices contains k vertex-disjoint monochromatic tight cycles that together cover n−o(n) vertices.

AB - A k-uniform tight cycle is a k-graph with a cyclic order of its vertices such that every k consecutive vertices from an edge. We show that for k≥3, every red-blue edge-coloured complete k-graph on n vertices contains k vertex-disjoint monochromatic tight cycles that together cover n−o(n) vertices.

UR - https://igt.centre-mersenne.org/

M3 - Article

JO - Innovations in Graph Theory

JF - Innovations in Graph Theory

ER -

Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

Abstract

Bibliographical note

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Projects

Ramsey theory: an extremal perspective

H2020_ERC_EXTCOMB

Matchings and tilings in graphs

Cite this