9 papers · 1 filter
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 labelled points on a circle by transpositions. Imagine that th…
Smaller universal posets
Paul Bastide, Carla Groenland, Rajko Nenadov
We show that there is a constant such that for each integer , there is a poset on at most elements that contains each -element poset as an (i…
Faithful universal graphs for minor-closed classes
Paul Bastide, Louis Esperet, Carla Groenland +3
It was proved by Huynh, Mohar, Šámal, Thomassen and Wood in 2021 that any countable graph containing every countable planar graph as a subgraph has an infinite clique minor. We p…
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…
Cube Height, Cube Width and Related Extremal Problems for Posets
Paul Bastide, JÄdrzej Hodor, Hoang La +1
Given a poset , a family of sets indexed by the elements of is called an inclusion representation of if in if and only if…
Path eccentricity of -AT-free graphs and application on graphs with the consecutive ones property
Paul Bastide, Claire Hilaire, Eileen Robinson
The central path problem is a variation on the single facility location problem. The aim is to find, in a given connected graph , a path minimizing its eccentricity, which i…