Thesiss

Linear Programming has been fruitful in designing approximation algorithms for many combinatorial optimization problems. Nonlinear programming did not receive as much attention in this respect until the recent work by Geomans and Williamson. They use semidefinite programs to obt…

A proper vertex coloring of a graph is an assignment of colors to all vertices such that adjacent vertices have distinct colors. The chromatic number χ(G) of a graph G is the minimum number of colors required for a proper vertex coloring. In this dissertation, we give some backg…