- Graph Theory: Fundamental concepts and basic definitions, path, cycles and trees, graph isomorphism, Eulerian and Hamiltonian graphs, planarity, connectivity, graph colourings, Euler's formula for planar graphs and proof of $5$ color theorem, matching, spectral graph theory; Numbered trees and Prufer code (if time permits).
- \bCombinatorics: Inclusion-exclusion principle, pigeon hole principle; Sperner's theorem, Hall marriage theorem; Mantel's theorem, Turan's theorem; graphic sequences (if time permits).
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