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Sorry for my English.

Here is the question:

Graph (V,E).

Definition: Legal's up-path in a graph from s to t is existent if and only if for every Vi, Vi+1 (for each i) fulfill w(Vi)<=w(Vi+1), when w(v) is a weight of the vertex.

We know that there is an algorithm like BFS that solve the problem of finding the shorter path in a Graph. We need to find, by reduction, an algorithm that solve the problem of legal's up-path.

I try to split each vertex, but it didn’t work (for example: for Vi=4, I tried to create 4 Edge, and then activate the BFS, but it didn’t work.

Thank u.

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up vote 1 down vote accepted

Assuming the BFS is for directed graphs, and you start with an undirected graph.

Hint: Try to pick a direction (and in some cases two) for each edge in the undirected graph so that the resulting graph is directed, and on which you can activate BFS.

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Thank u, but where you deal with the weight of the vertex? – user7734 Mar 3 '11 at 13:22
    
@Eyal: If I tell you it won't be a hint anymore! – Aryabhata Mar 3 '11 at 13:58
    
I got it.. Thank u – user7734 Mar 3 '11 at 18:53

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