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Combinatorics of Intervals

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Published on Apr 14, 2015

Speaker: András Gyárfás (Rényi Institute)

Abstract: Assume that J is a set of intervals on the real line. The following two important minimax theorems have been discovered by Tibor Gallai.

1. minimum number of partition classes of J into pairwise disjoint intervals = maximum number of pairwise intersecting members of J

2. minimum number of points piercing all members of J = maximum number of pairwise disjoint members of J

What happens if J is replaced by other structures? By subtrees of a tree? By arcs of a circle? By boxes? By intervals of the plane?

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