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Two-count interval representation of a permutation

Autor: Biró, Csaba, Kézdy, André E., Lehel, Jenő

The interval count problem, a classical question in the study of interval orders, was introduced by Ronald Graham in the 1980s. This problem asks: given an interval order $P$, what is the minimum number of distinct interval lengths required to constr

Externí odkaz: http://arxiv.org/abs/2411.11133

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The length polyhedron of an interval order

Autor: Biró, Csaba, Kézdy, André E., Lehel, Jenő

The length polyhedron $Q_P$ of an interval order $P$ is the convex hull of integral vectors representing the interval lengths in interval representations of $P$. This polyhedron has been studied by various authors, including Fishburn and Isaak. Notab

Externí odkaz: http://arxiv.org/abs/2410.21468

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An asymptotic resolution of a conjecture of Szemer\'{e}di and Petruska

Autor: Kézdy, André E., Lehel, Jenő

Consider a $3$-uniform hypergraph of order $n$ with clique number $k$ such that the intersection of all its $k$-cliques is empty. Szemer\'edi and Petruska proved $n\leq 8m^2+3m$, for fixed $m=n-k$, and they conjectured the sharp bound $n \leq {m+2 \c

Externí odkaz: http://arxiv.org/abs/2208.11573

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The equivalence of the Szemer\'edi and Petruska conjecture and the maximum order of $3$-uniform $\tau$-critical hypergraphs

Autor: Kézdy, André E., Lehel, Jenő

Recently we asymptotically resolved the long-standing Szemer\'edi and Petruska conjecture. Several decades ago Gy\'arf\'as et al. observed, via a straightforward but unpublished argument, that this conjecture is equivalent to the problem of determini

Externí odkaz: http://arxiv.org/abs/2204.02859

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