Let T be a connected graph and z ∈ℤ between the closed interval of 1 and...

Let T be a connected graph and z ∈ℤ between the closed interval of 1 and the least degree of a vertex in T. Let a z - matching be a A ⊆ E s.t. there aren’t vertices with more than z edges in A. Let a z - cover be a X ⊆ E s.t. all vertices belong to at least z edges in X.

Let:

δ (T) = Max {|A| : A is a z - matching}

μ (T) = Min {|X| : X is a z - cover}

Show that δ (T) + μ (T) = zn

Expert Solution

Here, Proof is Given in Two way.

pfirst by induction and second in (b).

Colby Messinger answered 5 months ago

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