Lane H. Clark

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For an orientation G of a simple graph G,-Ni7 [x] denotes the vertex x together with all those vertices in ~ for which there are arcs directed toward x. A set S of vertices of ~ is an efficient dominating set (EDS) of G provided that [IqS[x]nS [ = 1 for every x in G. An efficiency of G is an ordered pair (~, S), where S is an EDS of the orientation ~ of G.(More)
Let b(n, k) denote the number of permutations of {1,. .. , n} with precisely k inversions. We represent b(n, k) as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for b(n, k)/n! for a range of k including the maximum of(More)
We partition the set of spanning trees contained in the complete graph Kn into spanning trees contained in the complete bipartite graph Ks,t. This classification shows that some properties of spanning trees in Kn can be derived from trees in Ks,t. We use Abel's binomial theorem and the formula for spanning trees in Ks,t to obtain a proof of Cayley's theorem(More)
The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent sets and dominating sets. The complexity of learning vertex sets of xed size is also investigated, and it is shown that(More)