Publisher DOI: 10.1016/j.ejc.2017.12.006
Title: Colourings without monochromatic disjoint pairs
Language: English
Authors: Clemens, Dennis  
Das, Shagnik 
Tran, Tuan 
Issue Date: May-2018
Source: European Journal of Combinatorics (70): 99-124 (2018-05)
Abstract (english): 
The typical extremal problem asks how large a structure can be without containing a forbidden substructure. The Erdős–Rothschild problem, introduced in 1974 by Erdős and Rothschild in the context of extremal graph theory, is a coloured extension, asking for the maximum number of colourings a structure can have that avoid monochromatic copies of the forbidden substructure. The celebrated Erdős–Ko–Rado theorem is a fundamental result in extremal set theory, bounding the size of set families without a pair of disjoint sets, and has since been extended to several other discrete settings. The Erdős–Rothschild extensions of these theorems have also been studied in recent years, most notably by Hoppen, Koyakayawa and Lefmann for set families, and Hoppen, Lefmann and Odermann for vector spaces. In this paper we present a unified approach to the Erdős–Rothschild problem for intersecting structures, which allows us to extend the previous results, often with sharp bounds on the size of the ground set in terms of the other parameters. In many cases we also characterise which families of vector spaces asymptotically maximise the number of Erdős–Rothschild colourings, thus addressing a conjecture of Hoppen, Lefmann and Odermann.
URI: http://hdl.handle.net/11420/2947
ISSN: 0195-6698
Institute: Mathematik E-10 
Document Type: Article
Journal: European journal of combinatorics 
Appears in Collections:Publications without fulltext

Show full item record

Page view(s)

118
Last Week
1
Last month
1
checked on Jun 27, 2022

SCOPUSTM   
Citations

6
Last Week
0
Last month
0
checked on Jun 21, 2022

Google ScholarTM

Check

Add Files to Item

Note about this record

Cite this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.