József Balogh

activity

20232026

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7 papers · 1 filter

math.CO2026

Counting hypergraphs without linear cycles of fixed length

József Balogh, Ramon I. Garcia, Abhishek Methuku

Let $C_{k}^{(r)}$ be the $r$ -uniform linear cycle on $k$ hyperedges. An $r$ -graph is $C_{k}^{(r)}$ -free if it contains no copy of $C_{k}^{(r)}$ . Let $\operatorname{ex}_{r}(n,C_{k}^…

math.CO2026

Even smaller universal posets

József Balogh, Ramon I. Garcia, Marcelo Sales

We show that for every $η > 0$ and sufficiently large $n$ , there exists a poset of size $2^{(1 + η) n /2}$ containing all the $n$ -element posets as induced subposets. This improves a rec…

math.CO2025

Packing edge disjoint cliques in graphs

József Balogh, Michael C. Wigal

Let $r \geq 3$ be fixed and $G$ be an $n$ -vertex graph. A long-standing conjecture of Győri states that if $e (G) = t_{r - 1} (n) + k$ , where $t_{r - 1} (n)$ denotes the number of edges of…

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…

math.CO2023

Improving Uniquely Decodable Codes in Binary Adder Channels

József Balogh, The Nguyen, Patric R. J. Ostergard +2

We present a general method to modify existing uniquely decodable codes in the $T$ -user binary adder channel. If at least one of the original constituent codes does not have averag…

Counting hypergraphs without linear cycles of fixed length

Even smaller universal posets

Packing edge disjoint cliques in graphs

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

Improving Uniquely Decodable Codes in Binary Adder Channels

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