Question: Consider a complete bipartite graph whose vertices are partitioned into two subsets: V of size m and V2 of size n. Typically, we denote

Consider a complete bipartite graph whose vertices are partitioned into two subsets: V of size m and V2 of size n. Typically, we denote such a complete bipartite graph by Km,n. In a complete bipartite graph, every node in V is connected by an edge to every node in V2 (with no edges between nodes in the same partition). The following graph depicts K.1. 1 U5 V6 U2 V3 VA 1. How many Hamiltonian paths are there in K5,5 starting from a particular node s in one partition and ending in a particular node t in the other partition? 2. Suppose that we remove the edge (s, t) from K5,5. How many Hamiltonian paths are there from s to t in the resulting graph? 3. Suppose that we remove the edge (s, v) from K5,5 where 1. How many Hamiltonian paths are there from s to t in the resulting graph?

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