منابع مشابه
Random subgraphs make identification affordable
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the identifying code number (the size of a smallest identifying code), which indeed is not even a monotone parameter with respect to graph inclusion. We show that every...
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Understanding the subgraph distribution in random networks is important for modeling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as approximately N(n-g). However, many natural networks have a non-Poissonian degree distribution. Here we present approxima...
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A classical theorem by Erdős, Kleitman and Rothschild on the structure of triangle-free graphs states that with high probability such graphs are bipartite. Our first main result refines this theorem by investigating the structure of the ’few’ triangle-free graphs which are not bipartite. We prove that with high probability these graphs are bipartite up to a few vertices. Similar results hold if...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2017
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2017.v8.n1.a3