Finding the Most Vital Edges with Respect to the Number of Spanning Trees

@inproceedings{Tsen2004FindingTM,
  title={Finding the Most Vital Edges with Respect to the Number of Spanning Trees},
  author={Fu-Shang P. Tsen and Ting-Yi Sung and Men-Yang Lin and Lih-Hsing Hsu and Wendy Myrvold},
  year={2004}
}
Conclusions A most vital edge of a graph (w.r.t. the spanning trees) is an edge whose deletion most drastically decreases the number of spanning trees. We present an algorithm for determining the most vital edges based on Kirchoff’s matrixtree theorem whose asymptotic time-complexity can be reduced to that of the fastest matrix multiplication routine, currently O(n2.”$. The foundation for this approach is a more general algorithm for directed graphs for counting the rooted spanning… CONTINUE READING

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