Péter Hajnal

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Dirac's classical theorem asserts that, if every vertex of a graph G on n vertices has degree at least n2 then G has a Hamiltonian cycle. We give a fast parallel algorithm on a CREW PRAM to nd a Hamiltonian cycle in such graphs. Our algorithm uses a linear number of processors and is optimal up to a polylogarithmic factor. The algorithm works in O(log4 n)(More)
The arc-representation of a graph is a mapping from the set of vertices to the arcs of a circle such that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs having a point in common. The arc-width(aw) of a graph is the minimum width of its arc-representations. We show how arc-width is related(More)