Browsing by Author "Requile, Clement"
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Chordal graphs with bounded treewidth
Castellví Foguet, Jordi; Drmota, Michael; Noy Serrano, Marcos; Requile, Clement (Masaryk University, 2023)
Conference lecture
Open AccessGiven $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$connected chordal graphs with $n$ vertices and treewidth 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 (20230101)
Article
Open AccessWe 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 4regular planar graphs
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (20170801)
Article
Open AccessIn this extended abstract, we present the first combinatorial scheme for counting labeled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function ... 
Enumeration of labelled 4regular planar graphs II: asymptotics
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (202305)
Article
Open AccessThis work is a followup of the article (Noy et al., 2019), where the authors solved the problem of counting labelled 4regular planar graphs. In this paper, we obtain a precise asymptotic estimate for the number of labelled ... 
Enumeration of rooted 3connected bipartite planar maps
Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (20240307)
Article
Open AccessWe provide the first solution to the problem of counting rooted 3connected 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 (20220101)
Article
Open AccessA wellknown 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
BednarskaBzdega, Malgorzata; Krivelevich, Michael; Mészáros, Viola; Requile, Clement (201803)
Article
Open AccessWe consider the following twoplayer 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 policyThe 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 (20161018)
Article
Open AccessThe 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 (20230630)
Article
Open AccessWe 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, 20210901)
Part of book or chapter of book
Restricted access  publisher's policyA wellknown 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. (20151119)
Article
Open AccessThe 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 ...