Harry Metrebian

activity

20182022

collaborators

3 papers

math.CO2022

Odd colouring on the torus

Harry Metrebian

A proper vertex-colouring of a simple graph $G$ is said to be odd if, for every non-isolated vertex $v$ of $G$ , some colour appears an odd number of times in the neighbourhood of $…

math.CO2021

A New Upper Bound for the Ramsey Number of Fans

Vojtěch Dvořák, Harry Metrebian

A fan $F_{n}$ is a graph consisting of $n$ triangles, all having precisely one common vertex. Currently, the best known bounds for the Ramsey number $R (F_{n})$ are $9n/2-5 \leq R(F_n)…

math.CO2018

Tiling with punctured intervals

Harry Metrebian

It was shown by Gruslys, Leader and Tan that any finite subset of $Z^{n}$ tiles $Z^{d}$ for some $d$ . The first non-trivial case is the punctured interval, which cons…