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

Allan Lo; Vincent Pfenninger

doi:10.5817/CZ.MUNI.EUROCOMB23-100

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

Allan Lo
, Vincent Pfenninger

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

29 Downloads (Pure)

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
Title of host publication	EUROCOMB’23
Publisher	Masaryk University Press
Pages	1-6
Number of pages	6
DOIs	https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-100
Publication status	Published - 28 Aug 2023
Event	European Conference on Combinatorics, Graph Theory and Applications - Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic Duration: 28 Aug 2023 → 1 Sept 2023 https://iuuk.mff.cuni.cz/events/conferences/eurocomb23/

Publication series

Name	European Conference on Combinatorics, Graph Theory and Applications
Publisher	Masaryk University Press
Number	12
ISSN (Electronic)	2788-3116

Conference

Conference	European Conference on Combinatorics, Graph Theory and Applications
Abbreviated title	EUROCOMB'23
Country/Territory	Czech Republic
City	Prague
Period	28/08/23 → 1/09/23
Internet address	https://iuuk.mff.cuni.cz/events/conferences/eurocomb23/

Access to Document

10.5817/CZ.MUNI.EUROCOMB23-100Licence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

LoA2023AlmostFinal published version, 446 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

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
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

@inproceedings{86123b780c564be293795b376aedebdd,

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",

year = "2023",

month = aug,

day = "28",

doi = "10.5817/CZ.MUNI.EUROCOMB23-100",

language = "English",

series = "European Conference on Combinatorics, Graph Theory and Applications",

publisher = "Masaryk University Press",

number = "12",

pages = "1--6",

booktitle = "EUROCOMB{\textquoteright}23",

note = "European Conference on Combinatorics, Graph Theory and Applications, EUROCOMB'23 ; Conference date: 28-08-2023 Through 01-09-2023",

url = "https://iuuk.mff.cuni.cz/events/conferences/eurocomb23/",

}

Lo, A & Pfenninger, V 2023, Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles. in EUROCOMB’23., 100, European Conference on Combinatorics, Graph Theory and Applications, no. 12, Masaryk University Press, pp. 1-6, European Conference on Combinatorics, Graph Theory and Applications, Prague, Czech Republic, 28/08/23. https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-100

TY - GEN

T1 - Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

AU - Lo, Allan

AU - Pfenninger, Vincent

PY - 2023/8/28

Y1 - 2023/8/28

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.

U2 - 10.5817/CZ.MUNI.EUROCOMB23-100

DO - 10.5817/CZ.MUNI.EUROCOMB23-100

M3 - Conference contribution

T3 - European Conference on Combinatorics, Graph Theory and Applications

SP - 1

EP - 6

BT - EUROCOMB’23

PB - Masaryk University Press

T2 - European Conference on Combinatorics, Graph Theory and Applications

Y2 - 28 August 2023 through 1 September 2023

ER -

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

Abstract

Publication series

Conference

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Projects

Ramsey theory: an extremal perspective

Matchings and tilings in graphs

Cite this