Paul Bastide

activity

20242026

collaborators

8 papers

math.CO2026

Circular sorting, strong complete mappings and wreath product constructions

Paul Bastide, Anurag Bishnoi, Carla Groenland +2

We continue the study of Adin, Alon and Roichman [arXiv:2502.14398, 2025] on the number of steps required to sort $n$ labelled points on a circle by transpositions. Imagine that th…

math.CO2026

Smaller universal posets

Paul Bastide, Carla Groenland, Rajko Nenadov

We show that there is a constant $C > 0$ such that for each integer $n \geq 1$ , there is a poset on at most $2^{2 n /3 + C n}$ elements that contains each $n$ -element poset as an (i…

math.CO2026

Faithful universal graphs for minor-closed classes

Paul Bastide, Louis Esperet, Carla Groenland +3

It was proved by Huynh, Mohar, Å Ã¡mal, Thomassen and Wood in 2021 that any countable graph containing every countable planar graph as a subgraph has an infinite clique minor. We p…

cs.DS2025

Improved exploration of temporal graphs

Paul Bastide, Carla Groenland, Lukas Michel +1

A temporal graph $G$ is a sequence $(G_{t})_{t \in I}$ of graphs on the same vertex set of size $n$ . The \emph{temporal exploration problem} asks for the length of the shortest seque…

math.CO2025

Counterexamples to statements on isometric graph coverings

Paul Bastide, Julien Duron, JÄdrzej Hodor +2

A connected subgraph of a graph is isometric if it preserves distances. In this short note, we provide counterexamples to several variants of the following general question: When a…

math.CO2025

Cube Height, Cube Width and Related Extremal Problems for Posets

Paul Bastide, JÄdrzej Hodor, Hoang La +1

Given a poset $P$ , a family $S = {S_{x} : x \in P}$ of sets indexed by the elements of $P$ is called an inclusion representation of $P$ if $x ⩽ y$ in $P$ if and only if…