Group-harmonious labelings of trees

Organizers

Jie Ma , Benjamin Sudakov

Speaker

Alexey Pokrovskiy

Time

Tuesday, October 14, 2025 5:05 PM - 6:15 PM

Venue

Online

Zoom 787 662 9899 (BIMSA)

Abstract

Consider an order n abelian group G and a tree T on n vertices. When is it possible to (bijectively) label V(T) by G do that along all edges xy, the sums x+y are distinct? There are various motivations for studying this question, such as the Harmonious Labelling Conjecture of Graham-Sloane, which asks something related for cyclic G. This talk will be about giving a necessary and sufficient condition for the labelling to be possible in the case of arbitrary G and large, bounded degree T.
Joint work with Alp Müyesser.

Speaker Intro

Alexey Pokrovskiy completed his PhD on the topic of "Graph Powers, Partitions, and other Extremal Problems" under the supervision of Jozef Skokan and Jan van den Heuvel. Since then, he has continued working on extremal combinatorics particularly on the areas of Ramsey theory, Latin squares, and positional games. Prior to joining UCL he was a postdoc at Freie Universitat Berlin and ETH Zurich, and a lecturer at Birkbeck College. Currently he is a lecturer at University College London, and works on problems in-between combinatorics and algebra. In 2019 he received the European Prize in Combinatorics jointly with Richard Montgomery.