The poset of bipartitions

Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size [Formula: see text] for...

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2 00 9 the Poset of Bipartitions

Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size n form a graded lattice...

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2 1 Ju n 20 09 THE POSET OF BIPARTITIONS GÁBOR

Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size n form a graded lattice...

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On judicious bipartitions of graphs

For a positive integer m, let f(m) be the maximum value t such that any graph with m edges has a bipartite subgraph of size at least t, and let g(m) be the minimum value s such that for any graph G with m edges there exists a bipartition V (G) = V1 ∪ V2 such that G has at most s edges with both incident vertices in Vi. Alon proved that the limsup of f(m)− (m/2 + √ m/8) tends to infinity as m te...

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Bipartitions of highly connected tournaments

We show that if T is a strongly 10k log(2k)-connected tournament, there exists a partition A,B of V (T ) such that each of T [A], T [B] and T [A,B] is strongly k-connected. This provides solutions to tournament analogues of two partition conjectures of Thomassen regarding highly connected graphs. We also discuss spanning linkages as well as non-separating subdivisions in highly connected tourna...

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The poset of bipartitions

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