We sample directed graphs from asymmetric step-graphons and investigate the probability that the random digraph has at least one node-wise Hamiltonian decomposition. We show that for almost all step-graphons, the probability converges to either zero or one as the order of the digraph goes to infinity. We exhibit a set of conditions that can essentially decide the zero-one law, and numerically validate the result.
Publisher
Allerton Conference on Communication, Control, and Computing
Series/Report Name or Number
2025 61st Allerton Conference on Communication, Control, and Computing Proceedings
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