Let G be a graph. We say that a set of vertices C form a vertex cover if every edge of G is incident to at least one vertex in C. We say that a set of vertices I form an independent set if no edge in G connects two vertices from I.

Q: A path of length two is denoted by P2. If a graph G does not contain P2 as induced subgraph, then:…

A: Given:   A path of length two is denoted by P2. If a graph G does not contain P2 as induced…

Q: Hall’s

A:

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A: HI THEREI AM ADDING ANSWER BELOWPLEASE GO THROUGH ITTHANK YOU

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Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.