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Sphericity exceeds cubicity for almost all complete bipartite graphs

Hiroshi Maehara
1986 Journal of combinatorial theory. Series B (Print)  
We will prove that sphericity exceeds cubicity for complete bipartite graphs K(m, n) with max(m, n) > n" that sph K(n, n) > n, and that as a result of the latter there is a complete bipartite graph with  ...  sphericity exceeding cubicity for every value of cubicity at least 6.  ...  Have1 observed in [2] that cubicity can exceed sphericity.  ... 
doi:10.1016/0095-8956(86)90081-x fatcat:wzhh342cfjdlflfvh6qchunmiu

Lower Bounds for Boxicity [article]

Abhijin Adiga, L. Sunil Chandran, Naveen Sivadasan
2012 arXiv   pre-print
(where k is fixed) is Ω(k/ k). (5) There exists a positive constantc such that almost all balanced bipartite graphs on 2n vertices with exactly m edges have boxicity at least c m/n, for m< c' n^2/3 for  ...  On setting p=1/2 we immediately infer that almost all graphs have boxicity Ω(n). (3) Spectral lower bounds for the boxicity of k-regular graphs. (4) The boxicity of random k-regular graphs on n vertices  ...  Acknowledgements We thank Joel Friedman for personal communication regarding his proof of Alon's conjecture.  ... 
arXiv:0806.3175v2 fatcat:lypycwxyhzapheqdqsqbzz73bq

Page 2887 of Mathematical Reviews Vol. , Issue 87f [page]

1987 Mathematical Reviews  
Katona (Budapest) 87f:05158 Maehara, Hiroshi (J-RYK) 87f:05159 Sphericity exceeds cubicity for almost all complete bipartite graphs. J. Combin. Theory Ser. B 40 (1986), no. 2, 231-235.  ...  Hedetniemi proved that for a given graph H, there is a connected graph G whose order exceeds that of H by at most 4 and such that C(G) ~ H.  ... 

Impact of Clustering on the Performance of Network De-anonymization [article]

C.F Chiasserini and M. Garetto and E. Leonardi
2015 arXiv   pre-print
This procedure exploits an initial set of seed nodes large enough to trigger a percolation process which correctly matches almost all other nodes across the different social networks.  ...  Our main contribution is to show the crucial role played by clustering, which is a ubiquitous feature of realistic social network graphs (and many other systems).  ...  Indeed, a seed set whose size is equal to (nC k (n)) ǫ , for some ǫ, is enough to guarantee an almost complete successful network de-anonymization.  ... 
arXiv:1508.02017v1 fatcat:braph37pirawrhyw2duojhwl2q

Multicoloured Random Graphs: Constructions and Symmetry [article]

Sam Tarzi
2014 arXiv   pre-print
The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.  ...  This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants.  ...  (For example, W (BAut(R)) consists of all complete bipartite graphs and all unions of at most two complete graphs). These subspaces are invariant under the symmetric group.  ... 
arXiv:1406.7870v2 fatcat:othjxv7jzbhq7pupvjfmonunva

Provable Bounds for Learning Some Deep Representations [article]

Sanjeev Arora and Aditya Bhaskara and Rong Ge and Tengyu Ma
2013 arXiv   pre-print
Our algorithm learns almost all networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model.  ...  Our generative model is an n node multilayer neural net that has degree at most n^γ for some γ <1 and each edge has a random edge weight in [-1,1].  ...  In particular if d02 > n then almost all pairs are at distance 2 and the graph Ĝ given to us is simply a complete graph and thus reveals no information about G1 .  ... 
arXiv:1310.6343v1 fatcat:2s2634gpmrf4fp3gfqq3ngwmpm

Combinatorial complexity bounds for arrangements of curves and spheres

Kenneth L. Clarkson, Herbert Edelsbrunner, Leonidas J. Guibas, Micha Sharir, Emo Welzl
1990 Discrete & Computational Geometry  
We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike.  ...  For example, we prove that the maximum number of edges bounding m cells in an arrangement of n lines is O(m2/~n 2/~ + n), and that it is O(m2/an2/3~(n) + n) for n unit-circles, where p(n) (and later/~(  ...  Last but not least the authors are indebted to two anonymous referees for their careful reading of the paper and for their constructive criticism.  ... 
doi:10.1007/bf02187783 fatcat:cd46l3i2cney3bcsyzrk727b2u

Oscillation criteria for two-dimensional systems of first-order linear dynamic equations on time scales

Douglas Anderson, William Hall
2009 Involve. A Journal of Mathematics  
We also provide various results concerning the realizability of a graph as a zero-divisor graph.  ...  ideals based on their zero-divisor graphs.  ...  The remaining authors gratefully acknowledge the support of Amherst College: the Schupf Scholar Program for Krause, and Dean of Faculty student funds for Zhou.  ... 
doi:10.2140/involve.2009.2.1 fatcat:tar2csq4fvejzb5njizc47pa2q

The geometry of graphs and some of its algorithmic applications

Nathan Linial, Eran London, Yuri Rabinovich
1995 Combinatorica  
In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems.  ...  There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect the metric of the (possibly weighted) graph.  ...  Perles and Gil Kalai for stimulating discussions. Thanks are also due to Alex Samorodnitsky. We are particularly thankful to Leonid Levin for formulating Conjecture 8.1.  ... 
doi:10.1007/bf01200757 fatcat:lhkhob7abvhc7bhcfzyci7uqoy

Real-Time Path Planning for Coordinated Transport of Multiple Particles Using Optical Tweezers

Ashis Gopal Banerjee, Sagar Chowdhury, Wolfgang Losert, Satyandra K. Gupta
2012 IEEE Transactions on Automation Science and Engineering  
We use an iterative version of a maximum bipartite graph matching algorithm to assign given goal locations to such particles.  ...  This paper provides a step toward automating such manipulation operations by developing an intelligent planning framework that is geared for the unique characteristics of the microscopic environment and  ...  Ford-Fulkerson maximum flow algorithm [33] is applied to compute the maximum matching M for the bipartite graph.  ... 
doi:10.1109/tase.2012.2200102 fatcat:6shvd5wqlvbzjjjmptygsx2eay

The simplicial boundary of a CAT(0) cube complex

Mark F Hagen
2013 Algebraic and Geometric Topology  
the contact graph is bounded.  ...  For a CAT(0) cube complex X, we define a simplicial flag complex X, called the simplicial boundary, which is a natural setting for studying non-hyperbolic behavior of X.  ...  @ T X for each right-angled spherical simplex w of @ 4 X. Note that I.w/ is completely determined by fI.v i /g d iD0 .  ... 
doi:10.2140/agt.2013.13.1299 fatcat:wlrfchb4tnbydfvfryfijznsom

Large-scale automated identification of mouse brain cells in confocal light sheet microscopy images

Paolo Frasconi, Ludovico Silvestri, Paolo Soda, Roberto Cortini, Francesco S. Pavone, Giulio Iannello
2014 Computer applications in the biosciences : CABIOS  
Results: We introduce a fast and scalable algorithm for fully automated cell identification.  ...  ACKNOWLEDGMENTS We would like to thank Pietro Pala for useful discussions. Funding: The work of L.S. and F.P. was supported by E.U. grants FP7 228334, FP7 284464 and FET flagship HBP (604102).  ...  For this purpose, we first construct an undirected bipartite graph with vertex set C [ G. For each pair c ! 2 C and g ! 2 G we add an edge with weight w cg = 1 +k c ! À g ! k if k c ! À g !  ... 
doi:10.1093/bioinformatics/btu469 pmid:25161251 pmcid:PMC4147922 fatcat:m6r63cntozb6hbdwxvocfslbmu

Assortativity in complex networks

Rogier Noldus, Piet Van Mieghem
2015 Journal of Complex Networks  
In addition, the relation between assortativity and line graphs, complementary graphs and graph spectra needs further work, to incorporate directed graphs and weighted links.  ...  Since degree assortativity alone is not sufficient as a graph analysis tool, assortativity is usually combined with other graph metrics.  ...  Acknowledgement We thank Stojan Trajanovski for reviewing the paper and providing comments. References  ... 
doi:10.1093/comnet/cnv005 fatcat:4236bjleondk5foikgjc4yyrku

Self-avoiding walk enumeration via the lace expansion

Nathan Clisby, Richard Liang, Gordon Slade
2007 Journal of Physics A: Mathematical and Theoretical  
We obtain significant extensions of existing series on the cubic and hypercubic lattices in all dimensions d ≥ 3: we enumerate 32-step self-avoiding polygons in d = 3, 26-step self-avoiding polygons in  ...  d = 4, 30-step self-avoiding walks in d = 3, and 24-step self-avoiding walks and polygons in all dimensions d ≥ 4.  ...  All numerical calculations were performed using the computational resources of the Victorian Partnership for Advanced Computing (VPAC).  ... 
doi:10.1088/1751-8113/40/36/003 fatcat:cahgxdsw5vhxhje336cp5cjsre

An optimal sdp algorithm for max-cut, and equally optimal long code tests

Ryan O'Donnell, Yi Wu
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
All of the known lower bounds for Gap SDP (c) fall into the RPR 2 framework.  ...  focus attention in this work almost exclusively on the basic SDP (2).  ...  to be bipartite, in the Grothendieck case.  ... 
doi:10.1145/1374376.1374425 dblp:conf/stoc/ODonnellW08 fatcat:2oexhfetvffyzhw3ijtpsik7ci
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