Sk Samim Islam

activity

20232026

collaborators

18 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)…

cs.DS2026

Solving Vertex Integrity Faster than $2^{n}$

Sandip Das, Sweta Das, Sk Samim Islam +3

Vertex Integrity is a classical graph parameter measuring the vulnerability of a network to vertex failures. We settle two fundamental questions concerning its exact exponential co…

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…

math.CO2026

Broadcast Domination Number is at Most Twice the Multipacking Number

Sk Samim Islam

For a graph $G = (V, E)$ with a vertex set $V$ and an edge set $E$ , a function $f : V \to {0, 1, 2, ..., d iam (G)}$ is called a \emph{broadcast} on $G$ . For e…

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…

cs.DM2026

On the Complexity of Hop Domination and 2-Step Domination in Graph Classes

Sandip Das, Sweta Das, Sk Samim Islam

The domination problem is a well-studied problem in graph theory. In this paper, we study two natural variants: the hop domination problem and the $2$ -step domination problem. Let…

math.CO2026

Parameterized complexity of $r$ -Hop, $r$ -Step, and $r$ -Hop Roman Domination

Sandip Das, Sweta Das, Sk Samim Islam

The \textsc{Dominating Set} problem is a classical and extensively studied topic in graph theory and theoretical computer science. In this paper, we examine the algorithmic complex…

cs.CC2026

On the complexity of Multipacking

Sandip Das, Sk Samim Islam, Daniel Lokshtanov

A \emph{multipacking} in an undirected graph $G = (V, E)$ is a set $M \subseteq V$ such that for every vertex $v \in V$ and for every integer $r \geq 1$ , the ball of radius $r$ around $v…

cs.DM2026

Multipacking on graphs and Euclidean metric space

Sk Samim Islam

A \emph{multipacking} in an undirected graph $G = (V, E)$ is a set $M \subseteq V$ such that for every vertex $v \in V$ and for every integer $r \geq 1$ , the ball of radius $r$ around…

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.CG2024

Multipacking in Euclidean Metric Space

Arun Kumar Das, Sandip Das, Sk Samim Islam +2

Here we study the multipacking problems for geometric point sets with respect to their Euclidean distances. We consider a set of $n$ points $P$ and define $N_{s} [v]$ as the subset of…

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_…

cs.DM2023

Relation between broadcast domination and multipacking numbers on chordal and other hyperbolic graphs

Sandip Das, Florent Foucaud, Sk Samim Islam +1

For a graph $G = (V, E)$ with a vertex set $V$ and an edge set $E$ , a function $f : V \to {0, 1, 2, ..., d iam (G)}$ is called a \emph{broadcast} on $G$ . For e…

cs.DM2023

Multipacking and broadcast domination on cactus graph and its impact on hyperbolic graph

Sandip Das, Sk Samim Islam

For a graph $G$ , $m p (G)$ is the multipacking number, and $γ_{b} (G)$ is the broadcast domination number. It is known that $m p (G) \leq γ_{b} (G)$ and $γ_{b} (G) \leq 2 m p (G) + 3$ for any graph…

math.CO2023

Burning a binary tree and its generalization

Sandip Das, Sk Samim Islam, Ritam M Mitra +1

Graph burning is a graph process that models the spread of social contagion. Initially, all the vertices of a graph $G$ are unburnt. At each step, an unburnt vertex is put on fire…

Almost Empty Monochromatic Polygons in Planar Point Sets

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

Solving Vertex Integrity Faster than 2n

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

Broadcast Domination Number is at Most Twice the Multipacking Number

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

On the Complexity of Hop Domination and 2-Step Domination in Graph Classes

Parameterized complexity of r-Hop, r-Step, and r-Hop Roman Domination

On the complexity of Multipacking

Multipacking on graphs and Euclidean metric space

On the Number of Almost Empty Monochromatic Triangles

Multipacking in Euclidean Metric Space

Growth Rate of the Number of Empty Triangles in the Plane

Relation between broadcast domination and multipacking numbers on chordal and other hyperbolic graphs

Multipacking and broadcast domination on cactus graph and its impact on hyperbolic graph

Burning a binary tree and its generalization

Solving Vertex Integrity Faster than $2^{n}$

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

Parameterized complexity of $r$ -Hop, $r$ -Step, and $r$ -Hop Roman Domination