Year: 2011
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Diaconis, Persi, Holmes, Susan, Janson, Svante
Institutions: Stanford University, Uppsala University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953315709