The complete bipartite graph kmn is a graph with m n, Mathematics

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The complete bipartite graph kmn is a graph with m n

The complete bipartite graph Km,n is a graph with m + n vertices. These vertices are divided into a set of size m and a set of size n. We call these sets the parts of the graph. Within each of these sets there are no edges. But between each pair of vertices in different sets, there is an edge. The graph K4,4 is pictured in part (d) of Figure 6.19.

(a) For what values of m and n is Km,n Eulerian?

(b) For which values of m and n is Km,n Hamiltonian?

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