Shagnik Das

collaborators

4 papers

math.CO2025

Odd-Ramsey numbers of Hamilton cycles

Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1

The odd-Ramsey number $r_{o dd} (n, H)$ of a graph $H$ , as introduced by Alon in his work on graph-codes, is the minimum number of colours needed to edge-colour $K_{n}$ so that ev…

math.CO2025

Frequent elements in union-closed set families

Shagnik Das, Saintan Wu

The Union-Closed Sets Conjecture asks whether every union-closed set family $F$ has an element contained in half of its sets. In 2022, Nagel posed a generalisation of thi…

math.CO2025

Bounded fractional intersecting families are linear in size

Niranjan Balachandran, Shagnik Das, Brahadeesh Sankarnarayanan

Using the sunflower method, we show that if $I^¸ \in (0, 1) \cap Q$ and $F$ is a $O (n^{1/3})$ -bounded $I^¸$ -intersecting family over $[n]$ , then $\lvert \mathcal{F}…

math.CO2024

Odd-Ramsey numbers of complete bipartite graphs

Simona Boyadzhiyska, Shagnik Das, Thomas Lesgourgues +1

In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs $H$ in $K_{n}$ , defined as the minimum number of colours needed to c…