Now showing items 1-12 of 12

    • Chordal graphs with bounded tree-width 

      Castellví Foguet, Jordi; Drmota, Michael; Noy Serrano, Marcos; Requile, Clement (Masaryk University, 2023)
      Conference lecture
      Open Access
      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 ...
    • Enumeration of chordal planar graphs and maps 

      Castellví Foguet, Jordi; Noy Serrano, Marcos; Requile, Clement (2023-01-01)
      Article
      Open Access
      We determine the number of labelled chordal planar graphs with n vertices, which is asymptotically for a constant and . We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically ...
    • Enumeration of labeled 4-regular planar graphs 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2017-08-01)
      Article
      Open Access
      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 ...
    • Enumeration of labelled 4-regular planar graphs II: asymptotics 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2023-05)
      Article
      Open Access
      This work is a follow-up of the article (Noy et al., 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 of labelled ...
    • Enumeration of rooted 3-connected bipartite planar maps 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2024-03-07)
      Article
      Open Access
      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, ...
    • On the expected number of perfect matchings in cubic planar graphs 

      Noy Serrano, Marcos; Rué Perna, Juan José; Requile, Clement (2022-01-01)
      Article
      Open Access
      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 Esperet et al. (Adv. Math. 2011). On the ...
    • Proper colouring Painter–Builder game 

      Bednarska-Bzdega, Malgorzata; Krivelevich, Michael; Mészáros, Viola; Requile, Clement (2018-03)
      Article
      Open Access
      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 ...
    • Random cubic planar graphs revisited 

      Rué Perna, Juan José; Noy Serrano, Marcos; Requile, Clement (Elsevier, 2016)
      Other
      Restricted access - publisher's policy
      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. ...
    • Random cubic planar graphs revisited 

      Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2016-10-18)
      Article
      Open Access
      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
    • Random cubic planar maps 

      Drmota, Michael; Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2023-06-30)
      Article
      Open Access
      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 ...
    • The expected number of perfect matchings in cubic planar graphs 

      Rué Perna, Juan José; Requile, Clement; Noy Serrano, Marcos (Birkhäuser, 2021-09-01)
      Part of book or chapter of book
      Restricted access - publisher's policy
      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 ...
    • Variants of plane diameter completion 

      Golovach, Petr; Requile, Clement; Thilikos, Dimitrios M. (2015-11-19)
      Article
      Open Access
      The Plane Diameter Completion problem asks, given a plane graph G and a positive integer d, if it is a spanning subgraph of a plane graph H that has diameter at most d. We examine two variants of this problem where the ...