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1.
We consider a randomized version of the greedy algorithm for finding a large matching in a graph. We assume that the next edge is always randomly chosen from those remaining. We analyze the performance of this algorithm when the input graph is fixed. We show that there are graphs for which this Randomized Greedy Algorithm (RGA) usually only obtains a matching close in size to that guaranteed by worst-case analysis (i.e., half the size of the maximum). For some classes of sparse graphs (e.g., planar graphs and forests) we show that the RGA performs significantly better than the worst-case. Our main theorem concerns forests. We prove that the ratio to maximum here is at least 0.7690…, and that this bound is tight. 相似文献
2.
We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006 相似文献
3.
Ethan D. Bloch 《Discrete and Computational Geometry》2006,35(2):311-328
In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature,
that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains
an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined
a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect.
The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence
based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies
a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least
3), such that χ(link(ηi, K)) = 2 for all i-simplices ηi of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial
complex has Euler characteristic zero. 相似文献
4.
We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting graph homomorphisms” [Random Structures Algorithms 17 (2000), 260–289]. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
5.
We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations. 相似文献
6.
7.
A repetitively pulsed (40 Hz) TE CO2 laser using an oxygen tolerant discharge scheme is described. Long lived (>105 shots) stable discharges at high pump energy density (200 J.l–1 atm–1) have been achieved both with and without the use of additive gases. 相似文献
8.
9.
P. E. Dyer 《Optical and Quantum Electronics》1982,14(4):327-330
The influence of interference due to weak reflections from anti-reflection coated surfaces in CO2 laser optics is discussed and analysed. In certain cases quite low reflection levels (1%) are shown to lead to uncertainties in the mirror transmission coefficient or produce a non-uniform power loading on the mirror surface, resulting in damage. 相似文献
10.
J. A. Dyer 《Israel Journal of Mathematics》1969,7(1):51-59
Conditions for the embedding of a Banach space as a dense subspace of a continuous function space are studied. Necessary and
sufficient conditions for a Banach space to be isomorphic to aP
1 space are found. 相似文献