[algogeeks] Re: Graph theoretic problem

2008-02-05 Thread dor
The term colouring is a little confusing (is this a problem you wrote yourself?). I suppose you mean: find a minimum cardinality set S such that for each vertex v, either v is in S or at least one of v's neighbours is in S. This problem is not equivalent to the maximum independent set problem. It

[algogeeks] Re: Graph theoretic problem

2008-02-05 Thread dor
Colorwave? This seems a rather obscure algorithm for maximum independent set (that is, if it is actually an algorithm for the max independent set). Also, minimum dominating set and maximum independent set are not the same problem (they are not equivalent problems). You might want to be a little mo

[algogeeks] Re: Loop-tree decomposition of sparse connected graph

2008-02-05 Thread dor
Have you tried google? For (1), delete that particular edge and test whether the resulting graph is connected (i.e., do a depth-first search). This solution is optimal if you want to check whether removing a particular edge disconnects the graph. In the slightly more general case in which you wan

[algogeeks] Loop-tree decomposition of sparse connected graph

2008-02-05 Thread Jake
Hey, I have a couple questions concerning graph theory. 1) If I have a connected graph G(V,E), how can I determine if the removal of a particular graph edge leaves the remaining graph still "connected"? I mean specifically, how do you test for this in a fast way? 2) Is there any robust free-wa