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The weightw(G) of a weighted graphG is the sum of the weights of its edges. In this paper, we prove, as conjectured in [2], that every 2-edge-connected weighted graph onn vertices contains a cycle of weight at least 2w(G)/(n−1).
The existence of a cycle in directed and undirected graphs can be determined by whether depth-first search (DFS) finds an edge that points to an ancestor of the current vertex (it contains a back edge). All the back edges which DFS skips over are part of cycles.
What Is a Cycle? In graph theory, a path that starts from a given vertex and ends at the same vertex is called a cycle.
Given a weighted graph (directed or undirected) I need to find the cycle of the graph with the maximum weight.
The weight of a cycle being the sum of the weight of the edges of the graph.
It can be any cycle, not just base cycle for which we can
I could try to enumerate all cycles of the graph and then compute the maximum but the total number of cycles can be really big (if the graph is complete then any sequence of vertices where the first and last one are identical is a cycle).
Do you have any idea to find that maximum weight cycle without enumerating all cycles ?
If you need hypothesis on the graph (positives weights for example) please indicates them.
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