In this paper, a necessary condition for an arbitrary un-directed graph to have Hamilton cycle is proposed. Based on this condition, a mathematical solution for this problem is developed and several proofs and an algorithmic approach are introduced. The algorithm is successfully implemented on many...
I think it is not that simple, that algorithm works on an undirected graph but fails on directed graphs like 0-->1 | | v v 2-->3 The problem is that in your algorithm if you start at 0 then 3 will kinda look like a cycle, even though it's not. ...
An undirected biconnected graph G with nonnegative integer lengths on the edges is given. The problem we consider is that of finding a cycle basis B of G such that the length of the longest cycle included in B is the smallest among all cycle bases of G. We first observe that Horton's...
We devise a linear-time algorithm for finding an ambitus ín an undirected graph. An ambitus is a cycle in a graph containing two distinguished vertices such that certain different groups of bridges (called B itp -, B itQ -, and B itPQ -bridges) satisfy the property that a bridge in ...
An undirected biconnected graph G with nonnegative integer lengths on the edges is given. The problem we consider is that of finding a cycle basis B of G such that the length of the longest cycle included in B is the smallest among all cycle bases of G. We first observe that Horton's...
Using Lemma 1 we can shift our attention from a DCJ scenario on a set of pairs to a 2-break scenario on a junction graph J.Definition 8 (Maximum edge-disjoint cycle packing) An MECP of a graph G is a largest set of edge-disjoint cycles in G. If G is Eulerian, then an MECP co...
An approximation algorithm for finding a long path in Hamiltonian graphs The question we address in this paper is: Given an undirected graph that has Hamiltonian cycle, how long a path can one find in this graph, in polynomial time? B. Monien [7] first studied this problem and showed how...
Rules of every street challenge are run or cycle every single street of given (metropolitan) area which is usually a city or a neighborhood. Till this point the rules are simple and clear, but the problem is the street definition. How do we define a street? Do we include pedestrian paths...
A branch-and-cut algorithm for the undirected prize collecting traveling salesman problem Given an undirected graph with edge costs and vertex prizes, the aim of the Prize Collecting Traveling Salesman Problem (PCTSP) is to find a simple cycle m... JF Bérubé,M Gendreau,JY Potvin - 《Network...
If there is such a negative cycle, you can just traverse this cycle over and over, in each iteration making the cost of the path smaller. So you can make certain paths arbitrarily small, or in other words that shortest path is undefined. That automatically means that an undirected graph ...