منابع مشابه
On an Improved Definition of Embedding Degree
We demonstrate a fundamental flaw in the present definition of embedding degree for curves of any genus, and we present examples of elliptic curves and genus 2 curves which highlight the error. We explain how this can yield a dramatic (unbounded) difference between the size of the actual and presumed embedding fields. This observation has serious implications for the security of pairing-based c...
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We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facet degree sequences by considering arbitrary face-to-flag degree sequences. In particular, these may be viewed as natural refinements of the flag f -vector of the poset. We investigate properties and rel...
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A sequence 1l = (d 1 ,d 2 , ... ,d n) of positive integers is said to be graphic if there exists a simple graph G such that 1£ is the degree sequence of G. For a specified property P of graphs. a sequence 1l = (d 1 ,d 2 • ... • d n) of positive integers is said to be potentially P-graphic if 1l is graphic and there exists a realization of 1l with the property P. In this paper we characterize po...
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We introduce fractional realizations of a graph degree sequence and a closely associated convex polytope. Simple graph realizations correspond to a subset of the vertices of this polytope; we characterize degree sequences for which each polytope vertex corresponds to a simple graph realization. These include the degree sequences of threshold and pseudo-split graphs, and we characterize their re...
متن کاملOn realization graphs of degree sequences
Given the degree sequence d of a graph, the realization graph of d is the graph having as its vertices the labeled realizations of d, with two vertices adjacent if one realization may be obtained from the other via an edge-switching operation. We describe a connection between Cartesian products in realization graphs and the canonical decomposition of degree sequences described by R.I. Tyshkevic...
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ژورنال
عنوان ژورنال: Informatica
سال: 2019
ISSN: 1854-3871,0350-5596
DOI: 10.31449/inf.v43i1.2684