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Colorful fractional Helly theorem via weak saturation
Debsoumya Chakraborti, Minho Cho, Jinha Kim +1
Two celebrated extensions of the classical Helly's theorem are the fractional Helly theorem and the colorful Helly theorem. Bulavka, Goodarzi, and Tancer recently established the o…
Leray numbers of tolerance complexes
Minki Kim, Alan Lew
Let be a simplicial complex on vertex set . is called -Leray if the homology groups of any induced subcomplex of are trivial in dimensions and higher. is…
A system of disjoint representatives of line segments with given directions
Jinha Kim, Minki Kim, O-Joung Kwon
We prove that for all positive integers and , there exists an integer satisfying the following. If is a set of direction vectors in the plane and $\math…
Domination numbers and noncover complexes of hypergraphs
Jinha Kim, Minki Kim
Let be a hypergraph on a finite set . A {\em cover} of is a set of vertices that meets all edges of . If is not a cover of $\mathcal…
The layer number of -evenly distributed point sets
Ilkyoo Choi, Weonyoung Joo, Minki Kim
For a finite point set in , we consider a peeling process where the vertices of the convex hull are removed at each step. The layer number of a given point set…
Badges and rainbow matchings
Ron Aharoni, Joseph Briggs, Jinha Kim +1
Drisko proved that matchings of size in a bipartite graph have a rainbow matching of size . For general graphs it is conjectured that matchings suffice for this…