4 papers
Domination numbers and homotopy in certain ternary graphs
Taehyun Eom, Jinha Kim, Minki Kim
A ternary graph is a graph with no induced cycles of length modulo . It was recently shown that, if the independence complex of a ternary graph is not contractible, then it…
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…
Topology of independence complexes and cycle structure of hypergraphs
Jinha Kim
Recently, Zhang and Wu proved a conjecture of Kalai and Meshulam, showing that for every graph without induced cycles of length divisible by , the sum of all reduced Betti n…
Fractional Helly theorem for Cartesian products of convex sets
Debsoumya Chakraborti, Jaehoon Kim, Jinha Kim +2
Helly's theorem and its variants show that for a family of convex sets in Euclidean space, local intersection patterns influence global intersection patterns. A classical result of…