Given $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants ...

In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ...

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 number of edges and monochromatic edges, ...

We consider the following two-player game, parametrised by positive integers and . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph ...

The goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices

A well-known conjecture by Lovász and Plummer from the 1970s asserting that a bridgeless cubic graph has exponentially many perfect matchings was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other ...