M. Pasch

collaborators

3 papers

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 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.CO2025

Sharp thresholds for higher powers of Hamilton cycles in random graphs

TamÃ¡s 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…