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We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of(More)
It is known that evaluating the Tutte polynomial, T (G; x, y), of a graph, G, is #P-hard at all but eight specific points and one specific curve of the (x, y)-plane. In contrast we show that if k is a fixed constant then for graphs of tree-width at most k there is an algorithm that will evaluate the polynomial at any point using only a linear number of(More)
We introduce the greedy expectation algorithm for the fixed spectrum version of the frequency assignment problem. This algorithm was previously studied for the travelling salesman problem. We show that the domination number of this algorithm is at least σ n−⌈log 2 n⌉−1 where σ is the available span and n the number of vertices in the constraint graph. In(More)
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