← All courses K 5 K_5 K 5 Discrete and Data
Networks from the ground up: degrees and isomorphism, connectivity, trees and spanning trees, shortest paths and minimum spanning trees, Euler and Hamilton tours, matchings, planarity, coloring, network flows, and Ramsey theory.
What you'll be able to do
Model problems as graphs and prove facts with degree counting Run and justify BFS, Dijkstra, Kruskal and Prim Decide Eulerian, Hamiltonian, bipartite and planar questions Use Hall, max-flow min-cut, coloring bounds and Ramsey arguments Start the course
Go through each topic step by step — prose, worked examples, quick checks, and a timed practice round after every section.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics 1. Graphs and Degrees
6 lessons Vertices and edges, degree, the handshake lemma, and the graphs every course uses
2. Isomorphism and Subgraphs
6 lessons When two graphs are the same, and the invariants that prove they are not
3. Walks, Paths and Connectivity
6 lessons Walks and paths, components, counting walks with matrices, and weak points of a network
The many equivalent definitions of a tree, spanning trees, and counting labeled trees
5. Graph Algorithms
5 lessons Searching a graph, shortest paths, and minimum spanning trees
6. Eulerian and Hamiltonian Graphs
6 lessons Traversing every edge, visiting every vertex, and the theorems that decide when you can
7. Bipartite Graphs and Matchings
6 lessons Two-sided graphs, matchings, Hall's marriage theorem, and stable matchings
Drawing without crossings, Euler's formula, and the two forbidden graphs
9. Graph Coloring
6 lessons Chromatic number, greedy coloring, the chromatic polynomial, and edge coloring
10. Directed Graphs and Network Flows
6 lessons Digraphs and tournaments, strong connectivity, and the max-flow min-cut theorem
11. Extremal Graph Theory and Ramsey Theory
6 lessons How many edges force a triangle, and why complete disorder is impossible