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- Kunal Dutta, Esther Ezra, Arijit Ghosh
- Symposium on Computational Geometry
- 2015

We refine the bound on the packing number, originally shown by Haussler, for shallow geometric set systems. Specifically, let V be a finite set system defined over an n-point set X; we view V as a set of indicator vectors over the n-dimensional unit cube. A δ-separated set of V is a subcollection W, s.t. the Hamming distance between each pair u,v ∈ W is… (More)

- Kunal Dutta, Dhruv Mubayi, C. R. Subramanian
- SIAM J. Discrete Math.
- 2012

We obtain new lower bounds for the independence number of Kr-free graphs and linear kuniform hypergraphs in terms of the degree sequence. This answers some old questions raised by Caro and Tuza [7]. Our proof technique is an extension of a method of Caro and Wei [6, 20], and we also give a new short proof of the main result of [7] using this approach. As… (More)

Given a simple directed graph D = (V,A), let the size of the largest induced directed acyclic graph (dag) be denoted by mas(D). Let D ∈ D(n, p) be a random instance, obtained by choosing each of the ( n 2 ) possible undirected edges independently with probability 2p and then orienting each chosen edge independently in one of two possible directions with… (More)

- Kunal Dutta, Arijit Ghosh, Bruno Jartoux, Nabil H. Mustafa
- Symposium on Computational Geometry
- 2017

The packing lemma of Haussler states that given a set system (X,R) with bounded VC dimension, if every pair of sets in R have large symmetric difference, then R cannot contain too many sets. Recently it was generalized to the shallow packing lemma, applying to set systems as a function of their shallow-cell complexity. In this paper we present several new… (More)

- Kunal Dutta, C. R. Subramanian
- LATIN
- 2010

- Kunal Dutta, Arijit Ghosh
- ArXiv
- 2014

We prove a size-sensitive version of Haussler’s Packing lemma [7] for set-systems with bounded primal shatter dimension, which have an additional size-sensitive property. This answers a question asked by Ezra [9]. We also partially address another point raised by Ezra regarding overcounting of sets in her chaining procedure. As a consequence of these… (More)

- Arijit Bishnu, Kunal Dutta, Arijit Ghosh, Subhabrata Paul
- Discrete Mathematics
- 2016

A subset D ⊆ V of a graph G = (V,E) is a (1, j)-set if every vertex v ∈ V \D is adjacent to at least 1 but not more than j vertices in D. The cardinality of a minimum (1, j)-set of G, denoted as γ(1,j)(G), is called the (1, j)-domination number of G. Given a graph G = (V,E) and an integer k, the decision version of the (1, j)-set problem is to decide… (More)

- Kunal Dutta, Amritanshu Prasad
- J. Comb. Theory, Ser. A
- 2011

- Jeff Cooper, Kunal Dutta, Dhruv Mubayi
- Combinatorics, Probability & Computing
- 2014

Let G be a triangle-free graph with n vertices and average degree t. We show that G contains at least e(1−n −1/12) 1 2 n t ln t( 1 2 ln t−1) independent sets. This improves a recent result of the first and third authors [8]. In particular, it implies that as n → ∞, every triangle-free graph on n vertices has at least e(c1−o(1)) √ n lnn independent sets,… (More)

- Kunal Dutta, C. R. Subramanian
- SIAM J. Discrete Math.
- 2016