Let G be a graph of n nodes, and let k be a positive integer where 3 ≤ k ≤ n. A k-node hole in G is a cycle of k distinct nodes such that there are no edges between the nodes of that cycle, except for the edges that make up that cycle. Write a backtracking algorithm that generates all k-node holes in G, for a given k and G.
Let A[1:n, 1:n] be a matrix of positive real numbers. Write a backtracking algorithm that generates all permutations f of {1, 2, ..., n} where A[i, f(i)] < C, for some given input constant C.
