9 citations · 11 across the 6 of their papers we have counts for
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Almost Empty Monochromatic Polygons in Planar Point Sets
Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2
For integers , , and , let denote the smallest integer such that any set of at least points in th…
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 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)…
Solving Vertex Integrity Faster than
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…
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…
Almost Empty Monochromatic Triangles With Many Colors
Bhaswar B. Bhattacharya, Sandip Das, Sk Samim Islam +2
Given integers and , let denote the least integer such that every set of at least points in the plane, no three on a line…
An Improved Upper Bound for the Turán Number of the Hexagon
Sandip Das, Sk Samim Islam, Aashirwad Mohapatra +1
For a graph , the Turán number is the maximum number of edges in an -vertex graph containing no copy of . Determining the Turán numbers of even cy…
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…