3 citations · 3 across the 3 of their papers we have counts for
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Enumeration of rooted 3-connected bipartite planar maps
Marc Noy, Clément Requilé, Juanjo Rué
We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the…
Enumeration of chordal planar graphs and maps
Jordi Castellví, Marc Noy, Clément Requilé
We determine the number of labelled chordal planar graphs with vertices, which is asymptotically for a constant and . We a…
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…
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…