Skip to main content Accessibility help
×
Home
Hostname: page-component-cf9d5c678-vbn2q Total loading time: 0.379 Render date: 2021-07-26T21:23:35.916Z Has data issue: false Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

When is an Almost Monochromatic K4 Guaranteed?

Published online by Cambridge University Press:  01 November 2008

ALEXANDR KOSTOCHKA
Affiliation:
Department of Mathematics, University of Illinois, Urbana, USA and Institute of Mathematics, Novosibirsk, Russia (e-mail: kostochk@math.uiuc.edu)
DHRUV MUBAYI
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois, 851 S. Morgan Street, Chicago, IL 60607-704, USA (e-mail: mubayi@math.uic.edu)
Corresponding

Abstract

Suppose that n > (log k)ck, where c is a fixed positive constant. We prove that, no matter how the edges of Kn are coloured with k colours, there is a copy of K4 whose edges receive at most two colours. This improves the previous best bound of kck, where c′ is a fixed positive constant, which follows from results on classical Ramsey numbers.

Type
Paper
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Eichhorn, D. and Mubayi, D. (2000) Edge-coloring cliques with many colors on subcliques. Combinatorica 20 441444.CrossRefGoogle Scholar
[2]Erdös, P. (1981) Solved and unsolved problems in combinatorics and combinatorial number theory. Congressus Numerantium 32 4962.Google Scholar
[3]Erdös, P. and Gyárfás, A. (1997) A variant of the classical Ramsey problem. Combinatorica 17 459467.CrossRefGoogle Scholar
[4]Kostochka, A. and Rödl, V. (2001) On graphs with small Ramsey numbers. J. Graph Theory 37 198204.CrossRefGoogle Scholar
[5]Mubayi, D. (1998) Edge-coloring cliques with three colors on all 4-cliques. Combinatorica 18 293296.CrossRefGoogle Scholar
[6]Mubayi, D. (2004) An explicit construction for a Ramsey problem. Combinatorica 24 313324.CrossRefGoogle Scholar
[7]Sárközy, G. and Selkow, S. (2001) On edge colorings with at least q colors in every subset of p vertices. Electron. J. Combin. 8 R9.Google Scholar
[8]Sárközy, G. and Selkow, S. (2003) An application of the regularity lemma in generalized Ramsey theory. J. Graph Theory 44 3949.CrossRefGoogle Scholar
[9]Sudakov, B. (2003) A few remarks on Ramsey–Turán-type problems. J. Combin. Theory Ser. B 88 99106.CrossRefGoogle Scholar
6
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

When is an Almost Monochromatic K4 Guaranteed?
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

When is an Almost Monochromatic K4 Guaranteed?
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

When is an Almost Monochromatic K4 Guaranteed?
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *