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 ...

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 ...

This thesis mainly focuses on algorithmic and combinatorial questions related to some geometric problems on graphs. In the last part of this thesis, a graph coloring problem is also discussed. Boxicity and Cubicity: These ...

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 ...

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 ...