Saumya Sen

collaborators

8 papers

math.CO2026

Almost Empty Monochromatic Polygons in Planar Point Sets

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2

For integers $r \geq 3$ , $c \geq 2$ , and $s \geq 0$ , let $M_{r}^{⋆} (c, s)$ denote the smallest integer such that any set of at least $M_{r}^{⋆} (c, s)$ points in th…

math.CO2026

Strong Edge Colouring of Disk Graphs: A 6-Approximation and an Improved Unit-Disk Bound

Sandip Das, Sk Samim Islam, Aashirwad Mohapatra +2

A strong edge colouring of a graph $G$ is an edge colouring in which every colour class is an induced matching. The minimum number of colours is the strong chromatic index $χ'_s(G)…

math.CO2026

Large Planar Point Sets Contain 4 Collinear Points or Almost 7-Cliques, and Related Results

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2

We prove that every sufficiently large finite planar point set contains either four collinear points or seven points with at most one non-visible pair. More generally, we show that…

math.CO2026

Almost Empty Monochromatic Triangles With Many Colors

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2

Given integers $c \geq 2$ and $s \geq 0$ , let $M_{3} (c, s)$ denote the least integer such that every set of at least $M_{3} (c, s)$ points in the plane, no three on a line…

math.CO2026

An Improved Upper Bound for the Turán Number of the Hexagon

Sandip Das, Sk Samim Islam, Aashirwad Mohapatra +1

For a graph $F$ , the Turán number $ex (n, F)$ is the maximum number of edges in an $n$ -vertex graph containing no copy of $F$ . Determining the Turán numbers of even cy…

cs.DS2026

Minimum eccentricity shortest paths of $K_{2, 3}$ -minor-free graphs

Dibyayan Chakraborty, Sandip Das, Sk Samim Islam +2

Given a simple, undirected, and unweighted graph $G$ , and an integer $R$ , the objective of the \textsc{Minimum Eccentricity Shortest Path (MESP)} is to decide whether there exists…

math.CO2026

On the Number of Almost Empty Monochromatic Triangles

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +3

In this paper, we consider the problem of counting almost empty monochromatic triangles in colored planar point sets, that is, triangles whose vertices are all assigned the same co…

cs.DM2024

Growth Rate of the Number of Empty Triangles in the Plane

Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +1

Given a set $P$ of $n$ points in the plane, in general position, denote by $N_{Δ} (P)$ the number of empty triangles with vertices in $P$ . In this paper we investigate by how much $N_…

Almost Empty Monochromatic Polygons in Planar Point Sets

Strong Edge Colouring of Disk Graphs: A 6-Approximation and an Improved Unit-Disk Bound

Large Planar Point Sets Contain 4 Collinear Points or Almost 7-Cliques, and Related Results

Almost Empty Monochromatic Triangles With Many Colors

An Improved Upper Bound for the Turán Number of the Hexagon

Minimum eccentricity shortest paths of K2,3​-minor-free graphs

On the Number of Almost Empty Monochromatic Triangles

Growth Rate of the Number of Empty Triangles in the Plane

Minimum eccentricity shortest paths of $K_{2, 3}$ -minor-free graphs