MTL768: Graph Theory

3 Credits (3-0-0)

Overlaps with: MTL776

Introduction to Graphs: Definition and basic concepts; Trees: characterizations, counting of minimum spanning tree; Paths and Distance in Graphs: Basic Definitions, center and median of a graph, activity digraph and critical path; Eulerian Graphs: Definition and Characterization; Hamiltonian Graphs: Necessary and sufficient conditions, Planar Graphs: properties, dual, genus of a graph; Graph Coloring: vertex coloring, chromatic polynomials, edge coloring, planar graph coloring; Matching and Factorizations: maximum matching in bipartite graphs, maximum matching in general graphs, Hall’s marriage theorem, factorization; Networks: The Max-flow min-cut theorem, connectivity and edge connectivity, Menger’s theorem; Graph and Matrices.