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The Binomial Random Graph is a Bad Inducer
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DOI：10.1002/rsa.70067.png)
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Abstract
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For a finite graph and a value , let denote the largest for which there is a sequence of graphs of edge density approaching so that the induced -density of the sequence approaches . We show that for all on at least three vertices and all , the binomial random graph has induced -density strictly less than This provides a negative answer to a problem posed by Liu et al. (2023). Our approach is in the limiting setting of graphons, and we in fact show a stronger result: the binomial random graph is never a local maximum in the space of graphons of edge density . This is done by finding a sequence of balanced perturbations of arbitrarily small norm that increase the -density.
Keywords:
MULTIPLICITIES
INDUCIBILITY
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