E. Dahlhaus, P. Hajnal and M. Karpinski. On the Parallel Complexity of Hamiltonian Cycle and Matching Problem on Dense Graphs. J. Algorithms, 15, 367-384,  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Some progress in this direction was achieved with the sublinear time (O(n 2=3 log 3 n) parallel algorithm for bipartite matching due to Goldberg, Plotkin and Vaidya [8] NC algorithms have been obtained for some special cases of graphs; for instance, dense graphs (minimum degree at least n=2) [4], regular bipartite graphs [16] strongly chordal graphs [5] graphs with polynomially bounded number of perfect matchings [9] P4 tidy graphs[26] convex bipartite graphs [6] incomparability graphs [15] claw free graphs [3] and planar bipartite graphs [22] The problem of counting the number ....

E. Dahlhaus, P. Hajnal, and M. Karpinski. On the parallel complexity of Hamiltonian cycles and matching problem in dense graphs. Journal of Algorithms, 15:367-384, 1993.

....Suppose we are given a graph G with n vertices, and the minimum degree at least cn, c 2 [0; 1] is a xed constant. We call such a graph c dense. The classical theorem of Dirac [20] says that if c 2 , then G has a Hamilton cycle which can be found in polynomial time (even in the NC class [9]) Observe that the Hamilton cycle constitutes an optimal solution to all of the considered problems. That is why we assume c Previous results. 2 EC 2 VC: This is the simplest non trivial version of the connectivity problem and has been studied for a long time, but tight approximation ....

E. Dahlhaus, P. Hajnal and M. Karpinski. On the Parallel Complexity of Hamiltonian Cycle and Matching Problem on Dense Graphs. J. Algorithms, 15, 367-384,

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