Vertex Covers and Vertex Covering Numbers | Graph Theory

We introduce vertex covers, minimum vertex covers, and vertex covering numbers! We'll see some examples and non-examples of vertex covers, as well as minimum vertex covers and some that aren't minimum. The number of vertices in a minimum vertex cover is called the vertex covering number of the graph. We'll discuss why the complement of a vertex cover is an independent vertex set, and see how the covering number plus the independence number is the order of a graph (Gallai identity). We'll also discuss covering numbers of complete graphs, cycles, and complete bipartite graphs. #GraphTheory
A vertex is said to cover its incident edges. A set of vertices is a vertex cover is if covers every edge in the graph.
Independent Vertex Sets: • Independent Vertex Set...
Proof Complement of Vertex Cover is Independent Set: • Complement of Vertex C...
Proof Covering Number plus Independence Number is Order of Graph: (coming soon)
Graph Theory playlist: • Graph Theory
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