Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-l9xz9 Total loading time: 0.574 Render date: 2021-04-13T17:24:49.150Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Vicarious Graphs

Published online by Cambridge University Press:  13 November 2009

TOMASZ ŁUCZAK
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland (e-mail: tomasz@amu.edu.pl)
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: A.G.Thomason@dpmms.cam.ac.uk)
Corresponding

Abstract

Let H be some fixed graph. We call a graph Gvicarious for H if G is maximal H-free and, for every edge e of G, there is an edge f not in G such that Ge + f is also H-free. We demonstrate various properties of vicarious graphs and several examples are given. It is conjectured that a graph of order n which is vicarious for K3 has size at most (1/4 + o(1))().

Type
Paper
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below.

References

[1]Erdős, P. (1967) Some recent results on extremal problems in graph theory: Results. In Theory of Graphs, Proc. International Symposium, Rome 1966 (Rosenstiehl, P., ed.), Gordon and Breach, New York, Dunod, Paris, pp. 118123.Google Scholar
[2]Erdős, P. (1968) On some new inequalities concerning extremal properties of graphs. In Theory of Graphs, Proc. Colloquium, Tihany 1966 (Erdős, P. and Katona, G., eds), Academic Press, New York, pp. 7781.Google Scholar
[3]Erdős, P., Faudree, R. J., Gyárfás, A. and Schelp, R. H. (1991) Odd cycles in graphs of given minimum degree. In Graph Theory, Combinatorics and Applications, Vol. 1, Proc. International Conference, Kalamazoo 1988, Wiley-Interscience, New York, pp. 407418.Google Scholar
[4]Simonovits, M. (1968) A method for solving extremal problems in graph theory, stability problems. In Theory of Graphs, Proc. Colloquium, Tihany 1966 (Erdős, P. and Katona, G., eds), Academic Press, New York, pp. 279319.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 24 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 13th April 2021. This data will be updated every 24 hours.

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.

Vicarious Graphs
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.

Vicarious Graphs
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.

Vicarious Graphs
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *