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Empirical Studies of Load Generation for Data Center Networks
Data center networks form the backbone for modern Internet giants like Google, Facebook, Microsoft, and Amazon. Such networks consist of a layer of a large number of storage and compute servers connected through two or ...
Acyclic Edge Coloring Of Graphs
(2013-10-07)
A proper edge coloring of G =(V,E)is a map c : E → C (where C is the set of available colors ) with c(e) ≠ c(ƒ) for any adjacent edges e,f. The minimum number of colors needed to properly color the edges of G, is called ...
Boxicity And Cubicity : A Study On Special Classes Of Graphs
(2014-06-02)
Let F be a family of sets. A graph G is an intersection graph of sets from the family F if there exists a mapping f : V (G)→ F such that, An interval graph is an intersection graph of a family of closed intervals on the ...
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 ...