Michał Seweryn, Dimension and standard examples in planar posets

Room B332 IBS (기초과학연구원)

The dimension of a poset is the least integer d such that the poset is isomorphic to a subposet of the product of d linear orders. In 1983, Kelly constructed planar posets of arbitrarily large dimension. Crucially, the posets in his construction involve large standard examples, the canonical structure preventing a poset from having small

Hyunwoo Lee (이현우), Reconstructing hypergraph matching polynomials

Room B332 IBS (기초과학연구원)

By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all nk2, one can reconstruct the matching polynomial of an n-vertex k-uniform hypergraph from the multiset of all induced sub-hypergraphs on k1kn+1 vertices. This generalizes the well-known result of

Nicola Lorenz, A Minor Characterisation of Normally Spanned Sets of Vertices

Room B332 IBS (기초과학연구원)

A rooted spanning tree of a graph G is called normal if the endvertices of all edges of G are comparable in the tree order. It is well known that every finite connected graph has a normal spanning tree (also known as depth-first search tree). Also, all countable graphs have normal spanning trees, but uncountable

Eunjin Oh (오은진), Approximation Algorithms for the Geometric Multimatching Problem

Room B332 IBS (기초과학연구원)

Let S and T be two sets of points in a metric space with a total of n points. Each point in S and T has an associated value that specifies an upper limit on how many points it can be matched with from the other set. A multimatching between S and T is a way of pairing points such that each point in S is matched with at least as many

Seokbeom Kim (김석범), The structure of △(1, 2, 2)-free tournaments

Room B332 IBS (기초과학연구원)

Given a tournament S, a tournament is S-free if it has no subtournament isomorphic to S. Until now, there have been only a small number of tournaments S such that the complete structure of S-free tournaments is known. Let (1,2,2) be a tournament obtained from the cyclic triangle by substituting two-vertex tournaments for

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