Prove or disprove: (a) If G is a graph of order n and size m with...

Prove or disprove:
(a) If G is a graph of order n and size m with three cycles, then m ≥ n +
2.
(b) There exist exactly two regular trees.

Expert Solution

Colby Messinger answered 1 year ago

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

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Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where...

Prove or disprove each of the followings. If f(n) = ω(g(n)), then log2(f(n)) = ω(log2g(n)), where f(n) and g(n) are positive functions. ω(n) + ω(n2) = theta(n). f(n)g(n) = ω(f(n)), where f(n) and g(n) are positive functions. If f(n) = theta(g(n)), then f(n) = theta(20 g(n)), where f(n) and g(n) are positive functions. If there are only finite number of points for which f(n) > g(n), then f(n) = O(g(n)), where f(n) and g(n) are positive functions.

Question

Prove or disprove: (a) If G is a graph of order n and size m with...

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Expert Solution

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