Suppose that a graph G is such that each vertex of G has degree at least...

Suppose that a graph G is such that each vertex of G has degree at least 100. Show that G contains a cycle of length at least 101, i.e., a cycle passing through at least 101 vertices.

Expert Solution

Here a graph G(V, E) is such that each vertex of G has degree at least 100. it means that G has at least 101 vertices.

so we make cases

Case-I ) If G has 101 vertices & degree of each vertex is 100 ,So G become complete graph.

We know complete graph has a cycle contain 101 vertex has i.e G contain a cycle of length at least 101.

Case-II) If No. of vertex(V) in G has greater than 101 vertices.

[Note : If no. of vertex is less than 101 then graph G does not exist which contain degree of each vertex has 100.]

Colby Messinger answered 2 years ago

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