@MISC{Xu_judiciousk-partitions, author = {Baogang Xu and Xingxing Yu}, title = {Judicious k-partitions of graphs}, year = {} }

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Abstract

Judicious partition problems ask for partitions of the vertex set of graphs so that several quantities are optimized simultaneously. In this paper, we answer the following judicious partition question of Bollobás and Scott [6] in the affirmative: For any positive integer k and for any graph G of size m, does there exist a partition of V (G) into V1,..., Vk such that the total number of edges joining different Vi is at least k−1 k m, and for each i ∈ {1, 2,..., k} the total number of edges with both ends in Vi is at most m k − 1 k2 2k2 (√