NDLI: Judicious bisection of hypergraphs

Content Provider	Springer Nature Link
Author	Tang, Yu Cong Xu, Xin Wang, Guang Hui
Copyright Year	2016
Abstract	Judicious bisection of hypergraphs asks for a balanced bipartition of the vertex set that optimizes several quantities simultaneously. In this paper, we prove that if G is a hypergraph with n vertices and m i edges of size i for i = 1, 2, …, k, then G admits a bisection in which each vertex class spans at most $$\frac{{m1}}{2} + \frac{1}{4}{m_2} + \cdots + \left( {\frac{1}{{{2^k}}}} \right){m_k} + o\left( {{m_1} + \cdots + {m_k}} \right)$$ edges, where G is dense enough or Δ(G) = o(n) but has no isolated vertex, which turns out to be a bisection version of a conjecture proposed by Bollobás and Scott.
Ending Page	584
Page Count	6
Starting Page	579
File Format	PDF
ISSN	14398516
e-ISSN	14397617
Journal	Acta Mathematica Sinica, English Series
Issue Number	5
Volume Number	32
Language	English
Publisher	Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Publisher Date	2016-04-08
Publisher Place	Beijing
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Partition hypergraph judicious bisection Finite automorphism groups of algebraic, geometric, or combinatorial structures Finite geometries Block designs Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Judicious bisection of hypergraphs