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Satisfiability
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Monotone graph limits and quasimonotone graphs
Monotone graph limits and quasimonotone graphs,Bela Bollobas,Svante Janson,Oliver Riordan
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Monotone graph limits and quasimonotone graphs
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Bela Bollobas
,
Svante Janson
,
Oliver Riordan
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences $(G_n)$ of graphs in terms of a limiting object which may be represented by a
symmetric function
$W$ on $[0,1]$, i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show that the kernel is monotone (i.e., increasing in both variables) if and only if the sequence satisfies a `quasimonotonicity' property defined by a certain functional tending to zero. As a tool we prove an inequality relating the cut and $L^1$ norms of kernels of the form $W_1W_2$ with $W_1$ and $W_2$ monotone that may be of interest in its own right; no such inequality holds for general kernels.
Published in 2011.
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References
(18)
Moments of TwoVariable Functions and the Uniqueness of Graph Limits
(
Citations: 14
)
Christian Borgs
,
Jennifer Chayes
,
László Lovász
Journal:
Geometric and Functional Analysis  GEOM FUNCT ANAL
, vol. 19, no. 6, pp. 15971619, 2010
Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing
(
Citations: 42
)
C. Borgs
,
J. T. Chayes
,
L. Lovász
,
V. T. Sós
,
K. Vesztergombi
Journal:
Advances in Mathematics  ADVAN MATH
, vol. 219, no. 6, pp. 18011851, 2008
Threshold Graph Limits and Random Threshold Graphs
(
Citations: 14
)
Persi Diaconis
,
Susan Holmes
,
Svante Janson
Journal:
Internet Mathematics
, vol. 5, no. 3, pp. 267320, 2008
Graph limits and exchangeable random graphs
(
Citations: 33
)
Persi Diaconis
,
Svante Janson
Published in 2007.
EXTREMAL PROPERTIES OF RADEMACHER FUNCTIONS WITH APPLICATIONS TO THE KHINTCHINE AND ROSENTHAL INEQUALITIES
(
Citations: 33
)
T. FIGIEL
,
P. HITCZENKO
,
W. B. JOHNSON
,
G. SCHECHTMAN
,
J. ZINN
Published in 1997.
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Citations
(1)
Graphons, cut norm and distance, couplings and rearrangements
Svante Janson
Published in 2010.