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GRAPHONS, CUT NORM AND DISTANCE, COUPLINGS AND REARRANGEMENTS
, 2010
"... We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add various technical complements. We allow graphons on general probability spaces whenever possible. We ..."
Abstract

Cited by 13 (5 self)
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We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add various technical complements. We allow graphons on general probability spaces whenever possible. We also give some new results for {0,1}valued graphons.
Interval graph limits
, 2011
"... We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the c ..."
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Cited by 8 (5 self)
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We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits.