Minimum Guardians in Graphs

Description

This lecture discusses the concept of minimum guardians in graphs, where an independent set of edges is selected to minimize the number of guardians needed to monitor them. The instructor explains the process of selecting edges and placing guardians strategically to ensure efficient monitoring, highlighting the challenges in determining the minimum number of guardians required in certain scenarios.

Official source

https://mediaspace.epfl.ch/media/0_unv05kps

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In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.

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In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v.

Path (graph theory)

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