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Boxicity, Cubicity And Vertex Cover
(2010-09-28)
The boxicity of a graph G, denoted as box(G), is the minimum dimension d for which each vertex of G can be mapped to a d-dimensional axis-parallel box in Rd such that two boxes intersect if and only if the corresponding ...
Guarding Terrain using k-Watchtowers
The discrete k-watchtower problem for a polyhedral terrain T in R3 with n vertices is to
nd k vertical segments, called watchtowers, of smallest height, whose bottom end-points
(bases) lie on some vertices of T, and ...
Rainbow Colouring and Some Dimensional Problems in Graph Theory
(2018-04-05)
This thesis touches three different topics in graph theory, namely, rainbow colouring, product dimension and boxicity.
Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices ...
Problems on bend-number, circular separation dimension and maximum edge 2-colouring
Representation of graphs as the intersection graphs of geometric objects has a long
history. The objective is to a nd a collection of \simple" sets S such that a given graph
G is its intersection graph. We are interested ...
On Dimensional Parameters Of Graphs And Posets
(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 ...
Intersection Graphs Of Boxes And Cubes
(2011-01-25)
A graph Gis said to be an intersection graph of sets from a family of sets if there exists a function ƒ : V(G)→ such that for u,v V(G), (u,v) E(G) ƒ (u) ƒ (v) ≠ . Interval graphs are thus the intersection graphs ...
Parameterized Complexity of Maximum Edge Coloring in Graphs
(2018-03-09)
The classical graph edge coloring problem deals in coloring the edges of a given graph with minimum number of colors such that no two adjacent edges in the graph, get the same color in the proposed coloring. In the following ...
Rainbow Connection Number Of Graph Power And Graph Products
(2014-09-09)
The minimum number of colors required to color the edges of a graph so that any two distinct vertices are connected by at least one path in which no two edges are colored the same is called its rainbow connection number. ...
The Isoperimetric Problem On Trees And Bounded Tree Width Graphs
(2010-08-26)
In this thesis we study the isoperimetric problem on trees and graphs with bounded treewidth. Let G = (V,E) be a finite, simple and undirected graph. For let δ(S,G)= {(u,v) ε E : u ε S and v ε V – S }be the edge boundary ...
Hadwiger's Conjecture On Circular Arc Graphs
(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 ...