Fair representation by independent sets

Ron Aharoni; Noga Alon; Eli Berger; Maria Chudnovsky; Dani Kotlar; Martin Loebl; Ran Ziv

doi:10.1007/978-3-319-44479-6_2

Fair representation by independent sets

Ron Aharoni, Noga Alon, Eli Berger, Maria Chudnovsky, Dani Kotlar, Martin Loebl, Ran Ziv

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

11 Scopus citations

Abstract

For a hypergraph H let β(H) denote the minimal number of edges from H covering V(H). An edge S of H is said to represent fairly (resp. almost fairly) a partition (V₁, V₂, …, V_m) of for all i ≤ m. In matroids any partition of V(H) can be represented fairly by some independent set. We look for classes of hypergraphs H in which any partition of V(H) can be represented almost fairly by some edge.We show that this is true when H is the set of independent sets in a path, and conjecture that it is true when H is the set of matchings in K_n;_n. We prove that partitions of E(K_n;_n) into three sets can be represented almost fairly. The methods of proofs are topological.

Original language	English (US)
Title of host publication	A Journey through Discrete Mathematics
Subtitle of host publication	A Tribute to Jiri Matousek
Publisher	Springer International Publishing
Pages	31-58
Number of pages	28
ISBN (Electronic)	9783319444796
ISBN (Print)	9783319444789
DOIs	https://doi.org/10.1007/978-3-319-44479-6_2
State	Published - Jan 1 2017

All Science Journal Classification (ASJC) codes

General Computer Science
General Economics, Econometrics and Finance
General Business, Management and Accounting
General Mathematics

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10.1007/978-3-319-44479-6_2

Cite this

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AU - Aharoni, Ron

AU - Alon, Noga

AU - Berger, Eli

AU - Chudnovsky, Maria

AU - Kotlar, Dani

AU - Loebl, Martin

AU - Ziv, Ran

PY - 2017/1/1

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Fair representation by independent sets

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