Finding unavoidable colorful patterns in multicolored graphs release_auoxvch6hbbd3ap6mbyatdlqsu

by Matthew Bowen and Ander Lamaison and Necati Alp Müyesser

Released as a article .

2018  

Abstract

Let χ be a coloring of the edges of a complete graph on n vertices into r colors. We call χ ε-balanced if all color classes have ε fraction of the edges. Fix some graph H, together with an r-coloring of its edges. Consider the smallest natural number R_ε^r(H) such that for all n≥ R_ε^r(H), all ε-balanced χ of K_n contain a subgraph isomorphic to H in its coloring. Bollobás conjectured a simple characterization of H for which R_ε^2(H) is finite, which was later proved by Cutler and Montágh. Here, we obtain a characterization for arbitrary values of r, discuss quantitative bounds, as well as generalizations to infinite graphs.
In text/plain format

Archived Files and Locations

application/pdf  423.0 kB
file_3r4dwkdvyranvaatuwzfs6nxty
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2018-09-11
Version   v2
Language   en ?
arXiv  1807.02780v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: d2e6c1b0-bd63-4f00-9148-9db68e3fe34d
API URL: JSON