Seonghyuk Im (임성혁), Large clique subdivisions in graphs without small dense subgraphs

Room B232 IBS (기초과학연구원)

What is the largest number $f(d)$ where every graph with average degree at least $d$ contains a subdivision of $K_{f(d)}$? Mader asked this question in 1967 and $f(d) = \Theta(\sqrt{d})$ was proved by Bollobás and Thomason and independently by Komlós and Szemerédi. This is best possible by considering a disjoint union of $K_{d,d}$. However, this

Seonghyuk Im (임성혁), A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

Room B332 IBS (기초과학연구원)

A linear $3$-graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices.  A linear $3$-graph is called a Steiner triple system if each pair of two distinct vertices belong to a unique edge. A simple greedy algorithm shows that every $n$-vertex Steiner triple system $G$ contains all

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