Hostname: page-component-784d4fb959-jtjl6 Total loading time: 0 Render date: 2025-07-16T20:30:00.171Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximizing Several Cuts Simultaneously

Published online by Cambridge University Press:  01 March 2007

DANIELA KÜUHN  and
DERYK OSTHUS
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)
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 2 , March 2007 , pp. 277 - 283
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. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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. 26 127–139.CrossRefGoogle Scholar
[3]Bollobás, B. and Scott, A. D. (1999) Exact bounds for judicious partitions. Combinatorica 19 473–486.Google Scholar
[4]Bollobás, B. and Scott, A. D. (2002) Problems and results on judicious partitions. Random Struct. Alg. 21 414–430.CrossRefGoogle Scholar
[5]Bollobás, B. and Scott, A. D. (2004) Judicious partitions of bounded-degree graphs. J. Graph Theory 46 131–143.CrossRefGoogle Scholar
[6]Edwards, C. S. (1973) Some extremal properties of bipartite subgraphs. Canadian J. Math. 25 475–485.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. 8 131–147.3.0.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 29–43.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. 43 425–440.CrossRefGoogle Scholar
[12]Porter, T. D. (1992) On a bottleneck conjecture of Erdős. Combinatorica 12 317–321.CrossRefGoogle Scholar
[13]Porter, T. D. (1994) Graph partitions. J. Combin. Math. Combin. Comp. 15 111–118.Google Scholar
[14]Porter, T. D. (1999) Minimal partitions of a graph. Ars Combinatorica 53 181–186.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 23 321–324.3.0.CO;2-H>CrossRefGoogle Scholar