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Magazine Problem 31
Write a depth-first search algorithm to test whether a graph is connected.
Problem 32
Show that a tree is a bipartite graph.
Problem 33
Show that the vertices of a tree can be colored with two colors so that each edge is incident on vertices of different colors.
Problem 33
Show that a graph \(G\) with \(n\) vertices and fewer than \(n-1\) edges is not connected.
Problem 36
Show that a tree has either one or two centers.
Problem 38
Define the radius \(r\) of a tree using the concepts of eccentricity and center. The diameter \(d\) of any graph was defined before Exercise \(71,\) Section \(8.2 .\) Is it always true, according to your definition of radius, that \(2 r=d ?\) Explain.
Problem 38
Write a backtracking algorithm that outputs all subsets of \(\\{1,2, \ldots, n\\}\)
