637,829 research outputs found
Explicit Resolutions of Double Point Singularities of Surfaces
Locally analytically, any isolated double point occurs as a double covering
of a smooth surface. It can be desingularized via the canonical resolution, as
it is well-known. In this paper we explicitly compute the fundamental cycle of
both the canonical and minimal resolution of a double point singularity and we
classify those for which the fundamental cycle differs from the fiber cycle.
Finally we compute the conditions that a double point imposes to pluricanonical
systems.Comment: 31 pages; partially rewritte
Minimal Stable Sets in Tournaments
We propose a systematic methodology for defining tournament solutions as
extensions of maximality. The central concepts of this methodology are maximal
qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy
of tournament solutions, which encompasses the top cycle, the uncovered set,
the Banks set, the minimal covering set, the tournament equilibrium set, the
Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new
tournament solution, the minimal extending set, which is conjectured to refine
both the minimal covering set and the Banks set.Comment: 29 pages, 4 figures, changed conten
The Lifting Properties of A-Homotopy Theory
In classical homotopy theory, two spaces are homotopy equivalent if one space
can be continuously deformed into the other. This theory, however, does not
respect the discrete nature of graphs. For this reason, a discrete homotopy
theory that recognizes the difference between the vertices and edges of a graph
was invented, called A-homotopy theory [1-5]. In classical homotopy theory,
covering spaces and lifting properties are often used to compute the
fundamental group of the circle. In this paper, we develop the lifting
properties for A-homotopy theory. Using a covering graph and these lifting
properties, we compute the fundamental group of the 5-cycle , giving an
alternate approach to [4].Comment: 27 pages, 3 figures, updated version. Minor changes to the
introduction and clarification that the computation of the fundamental group
of the 5-cycle originally appeared in [4]. Title changed from "Computing
A-Homotopy Groups Using Coverings and Lifting Properties" to "The Lifting
Properties of A-Homotopy Theory
A Distributed algorithm to find Hamiltonian cycles in Gnp random graphs
In this paper, we present a distributed algorithm to find Hamiltonian cycles in random binomial graphs Gnp. The algorithm works on a synchronous distributed setting by first creating a small cycle, then covering almost all vertices in the graph with several disjoint paths, and finally patching these paths and the uncovered vertices to the cycle. Our analysis shows that, with high probability, our algorithm is able to find a Hamiltonian cycle in Gnp when p_n=omega(sqrt{log n}/n^{1/4}). Moreover, we conduct an average case complexity analysis that shows that our algorithm terminates in expected sub-linear time, namely in O(n^{3/4+epsilon}) pulses.Postprint (published version
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