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Award ID contains: 2426017

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  1. ; (, IFAC-PapersOnLine)
    We investigate the H-property for step-graphons. Specifically, we sample graphs G_n on n nodes from a step-graphon and evaluate the probability that G_n has a Hamiltonian decomposition in the asymptotic regime as n goes to infinity. It has been shown in our earlier work that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of the result and validate it through numerical studies. 
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    Free, publicly-accessible full text available January 1, 2026
  2. (, Washington University in St. Louis)
    Free, publicly-accessible full text available January 1, 2026