A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On finding a cycle basis with a shortest maximal cycle
Information Processing Letters
Efficient connectivity testing of hypercubic networks with faults
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Efficient deterministic algorithms for finding a minimum cycle basis in undirected graphs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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Given a set F of vertices of a connected graph G, we study the problem of testing the connectivity of G-F in polynomial time with respect to |F| and the maximum degree @D of G. We present two approaches. The first algorithm for this problem runs in O(|F|@D^2@e^-^1log(|F|@D@e^-^1)) time for every graph G with vertex expansion at least @e0. The other solution, designed for the class of graphs with cycle basis consisting of cycles of length at most l, leads to O(|F|@D^@?^l^/^2^@?log(|F|@D^@?^l^/^2^@?)) running time. We also present an extension of this method to test the biconnectivity of G-F in O(|F|@D^llog(|F|@D^l)) time.