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Sphericity exceeds cubicity for almost all complete bipartite graphs
1986
Journal of combinatorial theory. Series B (Print)
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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]
2012
arXiv
pre-print
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(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
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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]
2015
arXiv
pre-print
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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]
2014
arXiv
pre-print
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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]
2013
arXiv
pre-print
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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
1990
Discrete & Computational Geometry
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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
2009
Involve. A Journal of Mathematics
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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
1995
Combinatorica
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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
2012
IEEE Transactions on Automation Science and Engineering
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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
2013
Algebraic and Geometric Topology
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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
2014
Computer applications in the biosciences : CABIOS
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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
2015
Journal of Complex Networks
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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
2007
Journal of Physics A: Mathematical and Theoretical
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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
2008
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
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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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