Course Aim: Introduce students to basic concepts of graph theory, graph properties and formulations of typical graph problems. This is also supplemented with some abstract-level algorithms for the presented problems and with some advanced graph theory topics.
Main Topics: Simple graphs - digraphs - Eulerian and Hamiltonian graphs - trees - matchings - networks - paths - cycles - graph colorings - and planar graphs - existence - enumeration - construction - algorithms - optimization - pigeonhole principle - bijective combinatorics - inclusion-exclusion - recursions - graph modeling - isomorphism - degree sequences - edge counting - connectivity - Euler's formula - network flows and matching theory.