A necessary and sufficient condition for a graph to be minimally k-edge-connected where k is odd is presented. Based on this result, a divide-and-conquer algorithm to determine minimally k-edge-connected graphs is developed. Experiments are performed to check minimally 3-edge-connectivity. The results show that our algorithm is much more effective than the previously known best algorithm.
Ye, Yunming and Li, Yueping
"A new algorithm to determine minimally k-edgeconnected graphs with odd k,"
Applied Mathematics & Information Sciences: Vol. 07:
3, Article 16.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss3/16