József Balogh

activity

20232026

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3 papers · 1 filter

math.CO2024

Clique covers and decompositions of cliques of graphs

József Balogh, Jialin He, Robert A. Krueger +2

In 1966, Erdős, Goodman, and Pósa showed that if $G$ is an $n$ -vertex graph, then at most $⌊ n^{2} /4 ⌋$ cliques of $G$ are needed to cover the edges of $G$ , and the bound…

math.CO2024

On the number of $P$ -free set systems for tree posets $P$

József Balogh, Ramon I. Garcia, Michael C. Wigal

We say a finite poset $P$ is a tree poset if its Hasse diagram is a tree. Let $k$ be the length of the largest chain contained in $P$ . We show that when $P$ is a fixed tree poset,…

math.CO2024

Grid-drawings of graphs in three-dimensions

Jozsef Balogh, Ethan Patrick White

Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$ -degenerate graph on $n$ vertices can…

Clique covers and decompositions of cliques of graphs

On the number of P-free set systems for tree posets P

Grid-drawings of graphs in three-dimensions

On the number of $P$ -free set systems for tree posets $P$