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graph-theory

What a graph is

taught

Taught in

Requires

Nothing — this is foundational.

Required by

Local knowledge map

Local knowledge map

BFS and shortest paths in unweighted graphs Counting simple graphs by degree Counting the spanning trees of a small graph Counting trees versus counting graphs Dijkstra's algorithm Dual graphs Euler's formula for planar graphs: v - e + f = 2 Flow networks Generating sets and Cayley graphs Graph terminology and special graphs Greedy coloring Independent sets and cliques Kuratowski's theorem Matchings Strongly connected components The adjacency matrix and its eigenvalues The chromatic number Bipartite graphs Cayley graphs Counting labeled graphs Directed graphs Graph coloring Graph representations -- adjacency lists, adjacency matrices,… Graph traversal -- BFS and DFS Planar graphs and plane embeddings Simple graphs, multigraphs, loops What a graph is Counting by cases Cycles Degree of a vertex Generators of a group Subgraphs The product rule Tree traversal

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.