Arijit Ghosh

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20242026

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4 papers · 1 filter

math.CO2025

No Infinite $(p, q)$ -Theorem for Piercing Compact Convex Sets with Lines in $R^{3}$

Sutanoya Chakraborty, Arijit Ghosh

An infinite $(p, q)$ -theorem, or an $(ℵ_{0}, q)$ -theorem, involving two families $F$ and $G$ of sets, states that if in every infinite subset of $F$ ,…

math.CO2025

A geometric proof of the infinite $(p, q)$ -theorem for hyperplane piercing

Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi

We provide a geometric proof of the $(ℵ_{0}, d + 1)$ -theorem for piercing compact connected sets by hyperplanes. Our argument uses only elementary properties of convex sets and…

math.CO2025

Finite k-Transversals of Infinite Families of Fat Convex Sets

Sutanoya Chakraborty, Arijit Ghosh, Soumi Nandi

We prove an infinite $(p, q)$ -theorem for piercing fat compact convex sets in $\RR^d$ with $k$ -flats. Additionally, we develop a new framework through which infinite $(p, q)$ -theorem…

math.CO2024

A Hanani-Tutte Theorem for Cycles

Sutanoya Chakraborty, Arijit Ghosh

Given a drawing $D$ of a graph $G$ , we define the crossing number between any two cycles $C_{1}$ and $C_{2}$ in $D$ to be the number of crossings that involve at least one edge fro…

No Infinite (p,q)-Theorem for Piercing Compact Convex Sets with Lines in R3

A geometric proof of the infinite (p,q)-theorem for hyperplane piercing

Finite k-Transversals of Infinite Families of Fat Convex Sets

A Hanani-Tutte Theorem for Cycles

No Infinite $(p, q)$ -Theorem for Piercing Compact Convex Sets with Lines in $R^{3}$

A geometric proof of the infinite $(p, q)$ -theorem for hyperplane piercing