Zobrazeno 1 - 10
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pro vyhledávání: '"Requilé, Clément"'
Given $t\geq 2$ and $0\leq k\leq t$, 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 $c,\gamma >0$ dependin
Externí odkaz:
http://arxiv.org/abs/2301.00194
We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic planar maps, wh
Externí odkaz:
http://arxiv.org/abs/2209.14799
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, following Bernardi and Bousqu
Externí odkaz:
http://arxiv.org/abs/2202.13929
We determine the number of labelled chordal planar graphs with $n$ vertices, which is asymptotically $c_1\cdot n^{-5/2} \gamma^n n!$ for a constant $c_1>0$ and $\gamma \approx 11.89235$. We also determine the number of rooted simple chordal planar ma
Externí odkaz:
http://arxiv.org/abs/2202.13340
Publikováno v:
In Advances in Applied Mathematics June 2024 157
Publikováno v:
Publicacions Matem\`atiques, 2022, Vol. 66, N\'um. 1, p. 325-353
A well-known conjecture by Lov\'asz and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other hand, Chudnovsky and Se
Externí odkaz:
http://arxiv.org/abs/2005.13821
Publikováno v:
European Journal of Combinatorics Volume 110, May 2023, 103661
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 this paper, we obtain a precise asymptotic estimate for the number $g_n$
Externí odkaz:
http://arxiv.org/abs/2001.05943
The goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. In particular we cover tre
Externí odkaz:
http://arxiv.org/abs/1904.10244
Publikováno v:
In European Journal of Combinatorics May 2023 110
Publikováno v:
In Discrete Mathematics January 2023 346(1)