STEM / applied
Graph theory & combinatorics · Undergraduate · Math
Learning objectives from the Graph theory & combinatorics syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
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Undergraduate Graph Theory & Combinatorics — scope drawn from open graph theory texts and typical US combinatorics/graph theory syllabi.
Graph fundamentals
- Graphs and digraphs — Graphs and digraphs
- Basic terminology (vertices, edges, degree) — Basic terminology (vertices, edges, degree)
- Paths, cycles, and connectivity — Paths, cycles, and connectivity
- Components — Components
- Trees and spanning trees — Trees and spanning trees; Cayley's formula (statement)
- Euler trails and circuits — Euler trails and circuits; Hamilton paths and cycles
- Planar graphs — Planar graphs
- Euler's formula (introduction) — Euler's formula (introduction)
Counting and combinatorics
- Addition and multiplication principles — Addition and multiplication principles; permutations and combinations
- Binomial coefficients — Binomial coefficients
- Combinatorial identities — Combinatorial identities
- Inclusion–exclusion principle — Inclusion–exclusion principle
- Generating functions (introduction) — Generating functions (introduction)
- Recurrence relations — Recurrence relations
- Characteristic equations (introduction) — Characteristic equations (introduction)
Graph algorithms and structures
- Breadth-first and depth-first search — Breadth-first and depth-first search
- Shortest paths: Dijkstra's algorithm (introduction) — Shortest paths: Dijkstra's algorithm (introduction)
- Matchings — Matchings
- Hall's marriage theorem (statement) — Hall's marriage theorem (statement)
- Vertex and edge colorings — Vertex and edge colorings; chromatic number
- Ramsey theory (introduction) — Ramsey theory (introduction)
Learning objectives
Click an objective for study materials.
Graph fundamentals
- Graphs and digraphs — Graphs and digraphs
- Basic terminology (vertices, edges, degree) — Basic terminology (vertices, edges, degree)
- Paths, cycles, and connectivity — Paths, cycles, and connectivity
- Components — Components
- Trees and spanning trees — Trees and spanning trees; Cayley's formula (statement)
- Euler trails and circuits — Euler trails and circuits; Hamilton paths and cycles
- Planar graphs — Planar graphs
- Euler's formula (introduction) — Euler's formula (introduction)
Counting and combinatorics
- Addition and multiplication principles — Addition and multiplication principles; permutations and combinations
- Binomial coefficients — Binomial coefficients
- Combinatorial identities — Combinatorial identities
- Inclusion–exclusion principle — Inclusion–exclusion principle
- Generating functions (introduction) — Generating functions (introduction)
- Recurrence relations — Recurrence relations
- Characteristic equations (introduction) — Characteristic equations (introduction)
Graph algorithms and structures
- Breadth-first and depth-first search — Breadth-first and depth-first search
- Shortest paths: Dijkstra's algorithm (introduction) — Shortest paths: Dijkstra's algorithm (introduction)
- Matchings — Matchings
- Hall's marriage theorem (statement) — Hall's marriage theorem (statement)
- Vertex and edge colorings — Vertex and edge colorings; chromatic number
- Ramsey theory (introduction) — Ramsey theory (introduction)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Graph fundamentals
Graphs and digraphs
Coming soon - Counting and combinatorics
Addition and multiplication principles; permutations and combinations
Coming soon - Graph algorithms and structures
Breadth-first and depth-first search
Coming soon
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$1,162 · Graph theory & combinatorics · 18 tutoring hrs
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