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- W2743259196 abstract "Abstract For a simplicial complex C denote by β ( C ) the minimal number of edges from C needed to cover the ground set. If C is a matroid then for every partition A 1 , … , A m of the ground set there exists a set S ∈ C meeting each A i in at least | A i | β ( C ) elements. We conjecture a slightly weaker statement for the intersection of two matroids: if D = P ∩ Q , where P , Q are matroids on the same ground set V , and β ( P ) , β ( Q ) ≤ k , then for every partition A 1 , … , A m of the ground set there exists a set S ∈ D meeting each A i in at least 1 k | A i | − 1 elements. We prove that when m = 2 there is a set meeting each A i in at least ( 1 k − 1 | V | ) | A i | − 1 elements." @default.
- W2743259196 created "2017-08-17" @default.
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- W2743259196 date "2017-08-01" @default.
- W2743259196 modified "2023-09-27" @default.
- W2743259196 title "Fair representation in dimatroids" @default.
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- W2743259196 doi "https://doi.org/10.1016/j.endm.2017.06.014" @default.
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