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

Allan Lo; Vincent Pfenninger

doi:10.5802/igt.1

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

Allan Lo, Vincent Pfenninger

Mathematics

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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
Pages (from-to)	1-19
Number of pages	19
Journal	Innovations in Graph Theory
Volume	1
DOIs	https://doi.org/10.5802/igt.1
Publication status	Published - 27 Sept 2024

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10.5802/igt.1Licence: Creative Commons: Attribution (CC BY)

LoA2024AlmostFinal published version, 603 KBLicence: Creative Commons: Attribution (CC BY)

1 Finished
2 Active

Ramsey theory: an extremal perspective
Treglown, A. (Co-Investigator) & Lo, A. (Principal Investigator)
Engineering & Physical Science Research Council
1/01/22 → 31/12/24
Project: Research Councils
H2020_ERC_EXTCOMB
Osthus, D. (Co-Investigator) & Kuhn, D. (Principal Investigator)
European Commission
1/01/19 → 31/12/24
Project: EU
Matchings and tilings in graphs
Lo, A. (Co-Investigator) & Treglown, A. (Principal Investigator)
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.",

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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.

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JO - Innovations in Graph Theory

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

Abstract

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Projects

Ramsey theory: an extremal perspective

H2020_ERC_EXTCOMB

Matchings and tilings in graphs

Cite this