21 citations · 60 across the 13 of their papers we have counts for
5 papers · 2 filters
Limiting probabilities of first order properties of random sparse graphs and hypergraphs
Alberto Larrauri, Tobias Müller, Marc Noy
Let be the binomial random graph in the sparse regime, which as is well-known undergoes a phase transition at . Lynch (Random Structures Algorithms, 1992) s…
On the expected number of perfect matchings in cubic planar graphs
Marc Noy, Clément Requilé, Juanjo Rué
A well-known conjecture by Lovász and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Es…
Universal singular exponents in catalytic variable equations
Michael Drmota, Marc Noy, Guan-Ru Yu
Catalytic equations appear in several combinatorial applications, most notably in the numeration of lattice path and in the enumeration of planar maps. The main purpose of this pap…
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…
Enumeration of labelled 4-regular planar graphs II: asymptotics
Marc Noy, Clément Requilé, Juanjo Rué
This work is a follow-up of the article [Proc.\ London Math.\ Soc.\ 119(2):358--378, 2019], where the authors solved the problem of counting labelled 4-regular planar graphs. In th…