• Hadwiger's Conjecture On Circular Arc Graphs 

      Belkale, Naveen (2009-04-30)
      Conjectured in 1943, Hadwiger’s conjecture is one of the most challenging open problems in graph theory. Hadwiger’s conjecture states that if the chromatic number of a graph G is k, then G has a clique minor of size at ...
    • Hitting Geometric Range Spaces using a Few Points 

      Ashok, Pradeesha (2018-02-15)
      A range space (P, S) consists of a set P of n elements and a collection S = {S1,...,Sm} of subsets of P , referred to as ranges. A hitting set for this range space refers to a subset H of P such that every Si in S contains ...
    • Module Grobner Bases Over Fields With Valuation 

      Sen, Aritra (2017-07-12)
      Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical ...
    • On Dimensional Parameters Of Graphs And Posets 

      Adiga, Abhijin (2013-06-21)
      In this thesis we study the following dimensional parameters : boxicity, cubicity, threshold dimension and poset dimension. While the first three parameters are defined on graphs, poset dimension is defined on partially ...
    • On Linear Codes in Projective Spaces 

      Basu, Pranab
      The projective space $\mathbb{P}_q(n)$ of order $n$ over a finite field $\mathbb{F}_q$ is defined as the collection of all subspaces of the ambient space $\mathbb{F}_q^n$. The Grassmannian $\mathcal{G}_q(n, k)$ is the set ...