Shagnik Das

collaborators

4 papers

math.CO2026

Schur properties of randomly perturbed sets

Shagnik Das, Charlotte Knierim, Patrick Morris

A set $A$ of integers is said to be \emph{Schur} if any two-colouring of $A$ results in monochromatic $x, y$ and $z$ with $x + y = z$ . We study the following problem: how many random in…

math.CO2026

Vertex Ramsey properties of randomly perturbed graphs

Shagnik Das, Patrick Morris, Andrew Treglown

Given graphs $F, H$ and $G$ , we say that $G$ is $(F, H)_{v}$ -Ramsey if every red/blue vertex colouring of $G$ containsa red copy of $F$ or a blue copy of $H$ . Results of Åuczak, RuciÅ…

math.CO2026

On Balance, To What Degree is Burr's Conjecture True?

Shagnik Das, Bruce Reed, Jozef Skokan

For many trees $T$ , the Ramsey number of $T$ , denoted by $R (T)$ , is determined by the sizes of the partition classes in its unique bipartition. In 1976, Burr proved that…

math.CO2026

New results on the odd- and unique-Ramsey numbers

Shagnik Das, Ying-Sian Wu

The odd-Ramsey number $r_{odd} (n, H)$ of a graph $H$ is the minimum number of colors needed to edge-color $K_{n}$ so that in every copy of $H$ some color occurs an odd number o…