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CG3 Graph Theory: Walks, Paths, Cycles, and Bridges

Graph Terminology. Walks, Trails, Circuits, Paths, Cycles, Bridges, Connected Components, Trees, and Forests are introduced. It is proved that (1) If you have a walk, you have a path, (2) an edge is a bridge if and only if it is not on any cycles. Subscribe ‪@Shahriari‬ for in-depth undergraduate math videos. 00:00 Introduction 00:22 Plan for the lecture 01:09 Definition: Simple Graph, Multigraph, General Graph (   • CG1 Graphs: Basic Vocabulary  ) 02:52 Definition: Open & Closed Walks, Trails, Paths, Circuits, Cycles 07:04 Summary: Paths, Cycles, Trails, Circuits, Walks 08:05 Lemma: If you have a walk, you have a path 08:39 How to best watch these videos? 09:08 Proof of the Lemma 11:24 Definition: Connected Components, Bridges, Connected Graphs 13:36 Lemma: An edge is a bridge iff that edge is not on any cycles 15:02 Proof of Lemma 17:08 Definition: Trees & Forests 17:36 Preview of Next Video: Characterizations of Trees (   • CG4 Graphs: Six Characterizations of ...  ) A series of lectures on graph theory as part of a full course on introductory combinatorics based on my book Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022. DOI: https://doi.org/10.1017/9781108568708 For an annotated list of available videos for Combinatorics see https://pomona.box.com/s/by2ay2872avx... YouTube Playlist:    • Combinatorics, An Invitation   Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA