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4 papers
Cycles of given lengths in unicyclic components in sparse random graphs
Marc Noy, Vonjy Rasendrahasina, Vlady Ravelomanana +1
Let be subset of and let be the number of cycles belonging to unicyclic components whose length is in in the random graph . We find…
On strong infinite Sidon and sets and random sets of integers
David Fabian, Juanjo Rué, Christoph Spiegel
A set of integers is an -strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on , more specifically if $…
An Erdős--Fuchs Theorem for Ordered Representation Functions
Gonzalo Cao-Labora, Juanjo Rué, Christoph Spiegel
Let be a positive integer. We study concentration results for the ordered representation functions $r^{\leq}_k(A,n) = \# \big\{ (a_1 \leq \dots \leq a_k) \in A^k : a_1+\d…
Further results on random cubic planar graphs
Marc Noy, Clément Requilé, Juanjo Rué
We provide precise asymptotic estimates for the number of several classes of labelled cubic planar graphs, and we analyze properties of such random graphs under the uniform distrib…