What you'll learn

40 lessons in Graph theory

Graphs & basic propertiesEuler paths & circuitsTreesGraph coloring & the chromatic numberSpanning treesDFS, BFS & traversalsShortest pathsBipartite matchingDirected graphs & cyclesPlanar graphs & Euler's formulaGraph isomorphismNetwork flow & max-flow min-cutHamiltonian cycles & TSPStrongly connected componentsSpectral graph theoryExpander graphsProof: handshake lemmaProof of Euler's formula $V - E + F = 2$Proof: 6-color theorem (the easy one)Graph minors & Robertson-SeymourRandom graphsHall's marriage theorem & König's theoremConnectivity & Menger's theoremThe chromatic polynomialTurán's theorem & extremal graph theoryVizing's theorem & edge coloringCayley's formula & the Matrix-Tree theoremTutte's theorem & perfect matchingsTournamentsRamsey numbers & Ramsey theoryPerfect graphsSzemerédi's regularity lemmaKuratowski & Wagner: characterizing planarityList coloring & choosabilityCrossing numbers & the crossing lemmaGraph genus & surface embeddingsThe Lovász theta function & Shannon capacityWalks & powers of the adjacency matrixCentrality: four answers to one questionSmall worlds & scale-free graphs

How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Graph theory exactly where it's useful.

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Related Discrete Mathematics subjects

Combinatorics Boolean algebra & logic Order Theory Diophantine Approximation Algebraic Number Theory Discrete Math