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Sphericity exceeds cubicity for almost all complete bipartite graphs

1986
*
Journal of combinatorial theory. Series B (Print)
*

We will prove that

doi:10.1016/0095-8956(86)90081-x
fatcat:wzhh342cfjdlflfvh6qchunmiu
*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*. ...##
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Lower Bounds for Boxicity
[article]

2012
*
arXiv
*
pre-print

(where k is fixed) is Ω(k/ k). (5) There exists a positive constantc such that

arXiv:0806.3175v2
fatcat:lypycwxyhzapheqdqsqbzz73bq
*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. ...##
###
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. ...##
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Impact of Clustering on the Performance of Network De-anonymization
[article]

2015
*
arXiv
*
pre-print

This procedure exploits an initial set of seed nodes large enough to trigger a percolation process which correctly matches

arXiv:1508.02017v1
fatcat:braph37pirawrhyw2duojhwl2q
*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. ...##
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Multicoloured Random Graphs: Constructions and Symmetry
[article]

2014
*
arXiv
*
pre-print

The large number of references should help in making this a resource

arXiv:1406.7870v2
fatcat:othjxv7jzbhq7pupvjfmonunva
*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. ...##
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Provable Bounds for Learning Some Deep Representations
[article]

2013
*
arXiv
*
pre-print

Our algorithm learns

arXiv:1310.6343v1
fatcat:2s2634gpmrf4fp3gfqq3ngwmpm
*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 . ...##
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Combinatorial complexity bounds for arrangements of curves and spheres

1990
*
Discrete & Computational Geometry
*

We present upper and lower bounds

doi:10.1007/bf02187783
fatcat:cd46l3i2cney3bcsyzrk727b2u
*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. ...##
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Oscillation criteria for two-dimensional systems of first-order linear dynamic equations on time scales

2009
*
Involve. A Journal of Mathematics
*

We also provide various results concerning the realizability of a

doi:10.2140/involve.2009.2.1
fatcat:tar2csq4fvejzb5njizc47pa2q
*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. ...##
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The geometry of graphs and some of its algorithmic applications

1995
*
Combinatorica
*

In this paper we explore some implications of viewing

doi:10.1007/bf01200757
fatcat:lhkhob7abvhc7bhcfzyci7uqoy
*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. ...##
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Real-Time Path Planning for Coordinated Transport of Multiple Particles Using Optical Tweezers

2012
*
IEEE Transactions on Automation Science and Engineering
*

We use an iterative version of a maximum

doi:10.1109/tase.2012.2200102
fatcat:6shvd5wqlvbzjjjmptygsx2eay
*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*. ...##
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The simplicial boundary of a CAT(0) cube complex

2013
*
Algebraic and Geometric Topology
*

the contact

doi:10.2140/agt.2013.13.1299
fatcat:wlrfchb4tnbydfvfryfijznsom
*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 . ...##
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Large-scale automated identification of mouse brain cells in confocal light sheet microscopy images

2014
*
Computer applications in the biosciences : CABIOS
*

Results: We introduce a fast and scalable algorithm

doi:10.1093/bioinformatics/btu469
pmid:25161251
pmcid:PMC4147922
fatcat:m6r63cntozb6hbdwxvocfslbmu
*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 ! ...##
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Assortativity in complex networks

2015
*
Journal of Complex Networks
*

In addition, the relation between assortativity and line

doi:10.1093/comnet/cnv005
fatcat:4236bjleondk5foikgjc4yyrku
*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 ...##
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Self-avoiding walk enumeration via the lace expansion

2007
*
Journal of Physics A: Mathematical and Theoretical
*

We obtain significant extensions of existing series on the

doi:10.1088/1751-8113/40/36/003
fatcat:cahgxdsw5vhxhje336cp5cjsre
*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). ...##
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An optimal sdp algorithm for max-cut, and equally optimal long code tests

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. ...

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