Show that a graph with at least 2k vertices is k-connected if and only if for...

Show that a graph with at least 2k vertices is k-connected if and only if for any two unrelated subsets X, Y of V, such that | X | = k = | Y |, there are k foreign paths between X and Y.

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Expert Solution

since, a graph is k connected if and only if it has k disjoint paths joining two arbitrary vedrtex sets say X and Y of size k each of many to many typeof which a vertex belongs to both the sets is valid as one vertex path.

Colby Messinger answered 1 hour ago

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