Skip to main content Accessibility help
×
Home
Hostname: page-component-59df476f6b-f4krk Total loading time: 0.232 Render date: 2021-05-17T23:48:09.307Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

Maximizing Several Cuts Simultaneously

Published online by Cambridge University Press:  01 March 2007

DANIELA KÜUHN
Affiliation:
School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
DERYK OSTHUS
Affiliation:
School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK (e-mail: kuehn@maths.bham.ac.uk, osthus@maths.bham.ac.uk)
Corresponding

Abstract

Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that, for both i = 1, 2, we have . This gives an approximate answer to a question of Bollobás and Scott. We also prove results about partitions into more than two vertex classes. Our proofs yield polynomial algorithms.

Type
Paper
Copyright
Copyright © Cambridge University Press 2006

Access options

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

References

[1]Alon, N. and Spencer, J. (2000) The Probabilistic Method, 2nd edn, Wiley-Interscience.CrossRefGoogle Scholar
[2]Bollobás, B. and Scott, A. D. (1993) Judicious partitions of graphs. Periodica Math. Hungar. 26 127139.CrossRefGoogle Scholar
[3]Bollobás, B. and Scott, A. D. (1999) Exact bounds for judicious partitions. Combinatorica 19 473486.Google Scholar
[4]Bollobás, B. and Scott, A. D. (2002) Problems and results on judicious partitions. Random Struct. Alg. 21 414430.CrossRefGoogle Scholar
[5]Bollobás, B. and Scott, A. D. (2004) Judicious partitions of bounded-degree graphs. J. Graph Theory 46 131143.CrossRefGoogle Scholar
[6]Edwards, C. S. (1973) Some extremal properties of bipartite subgraphs. Canadian J. Math. 25 475485.CrossRefGoogle Scholar
[7]Edwards, C. S. (1975) An improved lower bound on the number of edges in a largest bipartite subgraph. In Proc. 2nd Czech. Symposium on Graph Theory, Prague, pp. 167–181.Google Scholar
[8]Fundia, A. D. (1996) Derandomizing Chebyshev's inequality to find independent sets in uncrowded hypergraphs. Random Struct. Alg. 8 131147.3.0.CO;2-Z>CrossRefGoogle Scholar
[9]Kühn, D. and Osthus, D. (2003) Partitions of graphs with high minimum degree or connectivity. J. Combin. Ser. Theory B 88 2943.CrossRefGoogle Scholar
[10]Motwani, R. and Raghavan, P. (1995) Randomized Algorithms, Cambridge University Press.CrossRefGoogle Scholar
[11]Papadimitriou, C. H. and Yannakakis, M. (1991) Optimization, approximation, and complexity classes. J. Comput. System Sci. 43 425440.CrossRefGoogle Scholar
[12]Porter, T. D. (1992) On a bottleneck conjecture of Erdős. Combinatorica 12 317321.CrossRefGoogle Scholar
[13]Porter, T. D. (1994) Graph partitions. J. Combin. Math. Combin. Comp. 15 111118.Google Scholar
[14]Porter, T. D. (1999) Minimal partitions of a graph. Ars Combinatorica 53 181186.Google Scholar
[15]Rautenbach, D. and Szigeti, Z. (2004) Simultaneous large cuts. Manuscript.Google Scholar
[16]Stiebitz, M. (1996) Decomposing graphs under degree constraints. J. Graph Theory 23 321324.3.0.CO;2-H>CrossRefGoogle Scholar

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.

Maximizing Several Cuts Simultaneously
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.

Maximizing Several Cuts Simultaneously
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.

Maximizing Several Cuts Simultaneously
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *