scholarly journals Forcibly-biconnected Graphical Degree Sequences: Decision Algorithms and Enumerative Results

2019 ◽  
Vol 6 (2) ◽  
pp. 1-17
Author(s):  
Kai Wang ◽  
2007 ◽  
Vol 16 (6) ◽  
pp. 923-946 ◽  
Author(s):  
AMIN COJA-OGHLAN

We investigate the Laplacian eigenvalues of sparse random graphs Gnp. We show that in the case that the expected degree d = (n-1)p is bounded, the spectral gap of the normalized Laplacian $\LL(\gnp)$ is o(1). Nonetheless, w.h.p. G = Gnp has a large subgraph core(G) such that the spectral gap of $\LL(\core(G))$ is as large as 1-O (d−1/2). We derive similar results regarding the spectrum of the combinatorial Laplacian L(Gnp). The present paper complements the work of Chung, Lu and Vu [8] on the Laplacian spectra of random graphs with given expected degree sequences. Applied to Gnp, their results imply that in the ‘dense’ case d ≥ ln2n the spectral gap of $\LL(\gnp)$ is 1-O (d−1/2) w.h.p.


1981 ◽  
Vol 33 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Béla Bollobás

10.37236/3414 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Sarah Behrens ◽  
Catherine Erbes ◽  
Michael Ferrara ◽  
Stephen G. Hartke ◽  
Benjamin Reiniger ◽  
...  

A sequence of nonnegative integers is $k$-graphic if it is the degree sequence of a $k$-uniform hypergraph. The only known characterization of $k$-graphic sequences is due to Dewdney in 1975. As this characterization does not yield an efficient algorithm, it is a fundamental open question to determine a more practical characterization. While several necessary conditions appear in the literature, there are few conditions that imply a sequence is $k$-graphic. In light of this, we present sharp sufficient conditions for $k$-graphicality based on a sequence's length and degree sum.Kocay and Li gave a family of edge exchanges (an extension of 2-switches) that could be used to transform one realization of a 3-graphic sequence into any other realization. We extend their result to $k$-graphic sequences for all $k \geq 3$. Finally we give several applications of edge exchanges in hypergraphs, including generalizing a result of Busch et al. on packing graphic sequences.


Author(s):  
C. López-Casado ◽  
C. J. Pérez del Pulgar ◽  
E. Fernández ◽  
V. F. Muñoz ◽  
A. Castro-Tirado

This paper proposes the design and development of a scheduler for the GLORIA telescope network. This network, which main objective is to make astronomy closer to citizens in general, is formed by 18 telescopes spread over four continents and both hemispheres. Part of the management of this network is made by the network scheduler. It receives the observation requests made by the GLORIA users and then sends it to the most suitable telescope. A key module of the network scheduler is the telescope decision algorithm that makes possible to choose the best telescope, and thus avoiding offering an observation to a telescope that cannot execute it. This paper shows two different telescope decision algorithms: the first one is only based on weather forecast, meanwhile the second one uses fuzzy logic and information from each network telescope. Both algorithms were deployed in the GLORIA network. The achieved results coupled with a comparative of their performance is shown. Moreover, the network scheduler architecture, based on a hybrid distributed-centralized schema, is detailed.


1998 ◽  
Vol 18 (1) ◽  
pp. 49 ◽  
Author(s):  
Zofia Majcher ◽  
Jerzy Michael
Keyword(s):  

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