Standard syllabus
Graph theory & combinatorics · Undergraduate · Math
Topics
Graph fundamentals
- Graphs, digraphs, and basic terminology (vertices, edges, degree)
- Paths, cycles, connectivity, and components
- Trees and spanning trees; Cayley's formula (statement)
- Euler trails and circuits; Hamilton paths and cycles
- Planar graphs and Euler's formula (introduction)
Counting and combinatorics
- Addition and multiplication principles; permutations and combinations
- Binomial coefficients and combinatorial identities
- Inclusion–exclusion principle
- Generating functions (introduction)
- Recurrence relations and characteristic equations (introduction)
Graph algorithms and structures
- Breadth-first and depth-first search
- Shortest paths: Dijkstra's algorithm (introduction)
- Matchings and Hall's marriage theorem (statement)
- Vertex and edge colorings; chromatic number
- Ramsey theory (introduction)
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$1,162 · Graph theory & combinatorics · 18 tutoring hrs
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