7 papers
On Weighted Convex Graphs
Angshuman R. Goswami
The main objective of this paper is to develop Krein-Milman-type theorems and Ulam-type stability results for graphs. To establish these results, we introduce several meaningful de…
On characterizations, Decompositions, and Stability of Convex Sequences
Angshuman R. Goswami
This paper introduces new characterizations, decomposition theorems, and stability results for convex sequences. We show that a sequence is convex precisely when its epigraph satis…
Approximate monotonicity, subadditivity, and convexity in weighted topologies
Angshuman R. Goswami
The central question of this paper is the following: "If a topological space equipped with a weight function satisfies a certain property only approximately, can we recover the ori…
On Weighted Star--Convex Graphs
Angshuman R. Goswami
The primary objective of this paper is to investigate the notions of geometric and sequential convexity within a graph-theoretic framework, with the aim of examining various struct…
Some Stability Results on Graphs
Angshuman R. Goswami, Mahmood K. Shihab
The primary objective of this paper is to introduce Hyers-Ulam-type stability results for monotone, subadditive, and convex graphs. We consider their standard definitions in an app…
Partitioning to solve Bin Packing Problems
Angshuman Robin Goswami
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in th…