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Better Bounds for k-Partitions of Graphs

Published online by Cambridge University Press:  31 May 2011

BAOGANG XU  and
XINGXING YU
BAOGANG XU
Affiliation:
School of Mathematical Sciences, Nanjing Normal University, 1 Wenyuan Road, Yadong New District, Nanjing, 210046, China (e-mail: baogxu@njnu.edu.cn)
XINGXING YU
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA (e-mail: yu@math.gatech.edu)
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Abstract

Let G be a graph with m edges, and let k be a positive integer. We show that V(G) admits a k-partition V1, . . . Vk such that for i ∈ {1, 2, . . . k}, and , where e(Vi) denotes the number of edges with both ends in Vi and . This answers a problem of Bollobás and Scott [2] in the affirmative. Moreover, for i ∈ {1, 2, . . ., k}, which is close to being best possible and settles another problem of Bollobás and Scott [2].

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 4 , July 2011 , pp. 631 - 640
Copyright
Copyright © Cambridge University Press 2011

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References

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