Unit-I
Binomial coefficients, convexity. Inequalities: Jensen’s, AM-GM, Cauchy Schwarz. Graphs, subgraphs, connectedness.
| Course Name | Advanced Graph Theory |
| Course Code | 24MAT474 |
| Program | 5 Year Integrated MSc/ BSc. (H) in Mathematics with Minor in Data Science |
| Semester | Elective |
| Credits | 3 |
| Campus | Amritapuri |
Binomial coefficients, convexity. Inequalities: Jensen’s, AM-GM, Cauchy Schwarz. Graphs, subgraphs, connectedness.
Euler circuits, cycles, trees, bipartite graphs and other basic concepts.
Vertex colourings. Graphs with large girth and large chromatic number.
Extremal graph theory: Dirac’s theorem. Ore’s theorem. Mantel’s theorem. Turan’s theorem (several proofs including probabilistic and analytic).
Kovari- Sosuran theorem with applications to geometry. Erdos Stone theorem. Stability. Andrasfai-Erdos-Sos theorem.
Course Outcomes
CO-1: Understand the basic concepts of graphs and trees.
CO-2: Understand and apply the concepts of graph connectivity and shortest path problems.
CO-3: Understand and apply the concepts of matching problems in job assignments.
CO-4: Understand the concepts of vertex and edge colorings.
CO-5: Understand the concepts of planar graphs and dual graphs.
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