Graph Theory, Chapter 3: Connectivity (Diestel, 6th edition)
by Reinhard Diestel · University of Hamburg
The complete Connectivity chapter of the sixth edition, released free by the author: 2-connected graphs and blocks, the structure of 3-connected graphs, Menger's theorem, Mader's theorem, edge-disjoint spanning trees, linking pairs of vertices, plus exercises.
More resources on Connectivity
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Wikipedia: Connectivity (graph theory)
Encyclopedia article defining vertex and edge connectivity, cut vertices, bridges, and k-connected graphs, stating Menger's theorem and bounds relating connectivity to minimum degree. Useful as a terminology reference with citations into the graph theory literature.
Diestel Graph Theory
Official site for Reinhard Diestel's Springer graduate text, where the main text is readable free online and paid eBook editions add the full apparatus. It covers matching, connectivity, planarity, colouring, flows, extremal theory, and minors.
Applications of Flows and Cuts (Algorithms, chapter 11)
Answers the how-do-you-actually-compute-connectivity half of the topic note. Chapter from Erickson's free Illinois algorithms textbook whose opening sections reduce edge-disjoint and vertex-disjoint path counting to maximum flow, giving the constructive algorithmic side of Menger's theorem; later sections extend the machinery to matching.
Menger's Theorems and the Ear Lemma (Charles University, Lecture 8)
Lecture handout from Charles University's NDMI011 course containing a complete induction proof of the vertex form of Menger's theorem, its edge and global variants, and the ear lemma characterising 2-connected graphs.
Graph Theory Lecture 9: Connectivity II — Menger's Theorem and Network Flows
Ninety-nine-minute lecture recorded live at Hamburg University in 2023/24, following the sixth edition of Diestel's book: proofs of the vertex and edge forms of Menger's theorem, global versions, and the max-flow min-cut theorem.