M. Pasch

activity

20182026

most citedInference and mutual information on random factor graphs

4 citations · 6 across the 8 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.CO2026

Improved Universal Graphs for Trees

Julian Becker, Konstantinos Panagiotou, Matija Pasch

A graph $G$ is universal for a class of graphs $C$ , if, up to isomorphism, $G$ contains every graph in $C$ as a subgraph. In 1978, Chung and Graham asked for th…

math.CO2025

Sharp thresholds for higher powers of Hamilton cycles in random graphs

Tamás Makai, Matija Pasch, Kalina Petrova +1

For $k \geq 4$ , we establish that $p = (e / n)^{1/ k}$ is a sharp threshold for the existence of the $k$ -th power $H$ of a Hamilton cycle in the binomial random graph model. Our proof…

math.CO2024

Sharp Thresholds for Factors in Random Graphs

Fabian Burghart, Annika Heckel, Marc Kaufmann +2

Let $F$ be a graph on $r$ vertices and let $G$ be a graph on $n$ vertices. Then an $F$ -factor in $G$ is a subgraph of $G$ composed of $n / r$ vertex-disjoint copies of $F$ , if $r$ di…

math.CO2024

The hitting time of nice factors

Fabian Burghart, Marc Kaufmann, Noela Müller +1

Consider the random $u$ -uniform hypergraph (or $u$ -graph) process on $n$ vertices, where $n$ is divisible by $r > u \geq 2$ . It was recently shown that with high probability, as soon a…

math.CO2024

Loose Hamilton paths in the 3-uniform cube hypergraph

Oliver Cooley, Johannes Machata, Matija Pasch

It is well-known that the $d$ -dimensional hypercube contains a Hamilton cycle for $d \geq 2$ . In this paper we address the analogous problem in the $3$ -uniform cube hypergraph, a $3$ …

math.CO2023

The hitting time of clique factors

Annika Heckel, Marc Kaufmann, Noela Müller +1

In a recent paper, Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let $r \geq 3$ and let $n$ be divisible by $…