Ann Comb
2013[Mar]; 17
(1
): 27-52
PMID26405368
show ga
We work out a 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.
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