hamiltonian-cycle

In a "dense" graph, I am trying to construct a Hamiltonian cycle using Palmer's Algorithm . However, I need more explanation for this algorithm because it does not work with me when I implement it. It seems that there is an unclear part in Wikipedia's explanation. I would be thankful if someone explains it more clearly or give me some links to read. Here's the algorithm statement: Palmer (1997) describes the following simple algorithm for constructing a Hamiltonian cycle in a graph meeting Ore's condition. Arrange the vertices arbitrarily into a cycle, ignoring adjacencies in the graph. While

I'm having trouble finding a way to build a tree path from a list of related tuples? I only want a list of every path where each node is visited once, aka hamiltonian path. I keep getting close but missing some path. For example, let's say we have this list of connections: connections = [(1, 4), (1, 5), (2, 5), (3, 4), (4, 1), (4, 3), (4, 5), (5, 1), (5, 2), (5, 4)] desired output: [[1,4,3], [1,4,5,2], [1,5,2], [1,5,4,3], [2,5,1,4,3], [2,5,4,1], [2,5,4,3], [3,4,1,5,2], [3,4,5,1], [3,4,5,2], [4, 3], [4,1,5,2], [4,5,1], [4,5,2], [5, 2], [5,1,4,3], [5,4,1], [5,4,3] ] So each possible path is

I am referring to Skienna's Book on Algorithms. The problem of testing whether a graph G contains a Hamiltonian path is NP-hard , where a Hamiltonian path P is a path that visits each vertex exactly once. There does not have to be an edge in G from the ending vertex to the starting vertex of P , unlike in the Hamiltonian cycle problem. Given a directed acyclic graph G ( DAG ), give an O(n + m) time algorithm to test whether or not it contains a Hamiltonian path. My approach, I am planning to use DFS and Topological sorting . But I didn't know how to connect the two concepts in solving the

Code jam problem is the following: You are given a complete undirected graph with N nodes and K "forbidden" edges. N <= 300, K <= 15. Find the number of Hamiltonian cycles in the graph that do not use any of the K "forbidden" edges. Unfortunately the explanations of this here on stack and throughout the web are very insufficient. I can figure out HamCycles for a certain 'n' : (n-1)! / 2 . And I can do the short set with dynamic programming. But I don't get all the subset bologna, how to make it O^K? I'm in Python and have yet to decipher the C++ available. Eventually I'm sure I will take the