Prove that every bipartite graph G with size m satisfies α prime(G) ≥ m/∆(G).

Expert Solution

ANSWER :-

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A bipartite graph is a special case of a k-partite graph.

From konjg's egevary theorem,

The size of the bipartite graph has a matching size at least

here we are having bipartite graph G with size m

let us consider prime(G) is a prime function of the bipartite graph.

But from konjg's egevary theoram ||G|| = m.

then.,

A bipartite graph is a special case of a k-partite graph.

prime(G) is always greater than the size of the graph.

that every bipartite graph G with size m satisfies α prime(G) ≥ m/∆(G).

since α prime(G) ≥ m/∆(G).

Hence proved.

Colby Messinger answered 2 years ago

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