Shagnik Das

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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.CO2024

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.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…

math.CO2024

Bounded fractional intersecting families are linear in size

Niranjan Balachandran, Shagnik Das, Brahadeesh Sankarnarayanan

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