2 citations · 3 across the 10 of their papers we have counts for
11 papers
Sharp quadratic -binding functions for powers of bipartite graphs
Arpan Sadhukhan, Suraj Kumar Sahoo
For every natural number , we construct powers of bipartite graphs whose chromatic number is quadratic in their clique number, showing that the straightforward qu…
Exact-Distance Domination in Grid Graphs
Sandip Das, Sweta Das, Arpan Sadhukhan
Let be the square grid, and let . A set is an \emph{exact-distance -dominating set} if every vertex has a…
Locating a Seymour vertex in oriented graphs having minimum outdegree at most 7
Arpan Sadhukhan, R. B. Sandeep, Sagnik Sen
A vertex of an oriented graph is a Seymour vertex if the number of outneighbors of is less than or equal to the number of second outneighbors of (vertices at direct…
The structure of -free tournaments
Seokbeom Kim, Taite LaGrange, Mathieu Rundström +2
We extend the list of tournaments for which the complete structural description for tournaments excluding as a subtournament is known. Specifically, let be a t…
Stable Approximation Algorithms for Dominating Set and Independent Set
Mark de Berg, Arpan Sadhukhan, Frits Spieksma
We study the Dominating set problem and Independent Set Problem for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is -sta…
On Stable Approximation Algorithms for Geometric Coverage Problems
Mark de Berg, Arpan Sadhukhan
Let be a set of points in the plane and let be an integer. The goal of Max Cover by Unit Disks problem is to place unit disks whose union covers the maximum number of p…
A Simple Construction of Tournaments with Finite and Uncountable Dichromatic Number
Arpan Sadhukhan
The dichromatic number of a digraph is the minimum number of colors needed to color the vertices in such a way that no monochromatic directed cy…
Shift Graphs, Chromatic Number and Acyclic One-Path Orientations
Arpan Sadhukhan
Shift graphs, which were introduced by Erdős and Hajnal, have been used to answer various questions in extremal graph theory. In this paper, we prove two new results using shift gr…
A Combinatorial Proof of the Existence of Dense subsets in R without the "Steinhaus" like Property
Arpan Sadhukhan
This paper proves the existence of nonmeasurable dense sets with additional properties using combinatorial techniques.
Stable Approximation Algorithms for the Dynamic Broadcast Range-Assignment Problem
Mark de Berg, Arpan Sadhukhan, Frits Spieksma
Let be a set of points in , where each point has an associated transmission range . The range assignment induces a directed communication graph…
An Alternative Proof of Steinhaus Theorem
Arpan Sadhukhan
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.