31 citations · 71 across the 14 of their papers we have counts for
18 papers
Maximal independent sets and maximal matchings in series-parallel and related graph classes
Michael Drmota, Lander Ramos, Clément Requilé +1
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…
Structure and enumeration of K4-minor-free links and link-diagrams
Juanjo Rué, Dimitrios M. Thilikos, Vasiliki Velona
We study the class L of link-types that admit a K4-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of K4.…
On a problem of Sárközy and Sós for multivariate linear forms
Juanjo Rué, Christoph Spiegel
We prove that for pairwise co-prime numbers there does not exist any infinite set of positive integers such that the representation function $r_A (n) = \…
On the optimality of the uniform random strategy
Christopher Kusch, Juanjo Rué, Christoph Spiegel +1
The concept of biased Maker-Breaker games, introduced by Chvátal and Erd{\H o}s, is a central topic in the field of positional games, with deep connections to the theory of random…
Enumeration of labelled 4-regular planar graphs
Marc Noy, Clément Requilé, Juanjo Rué
We present the first combinatorial scheme for counting labelled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential gen…
Counting configuration-free sets in groups
Juanjo Rué, Oriol Serra, Lluís Vena
We provide new examples of the asymptotic counting for the number of subsets on groups of given size which are free of certain configurations. These examples include sets without s…
Subgraph statistics in subcritical graph classes
Michael Drmota, Lander Ramos, Juanjo Rué
Let be a fixed graph and a subcritical graph class. In this paper we show that the number of occurrences of (as a subgraph) in a uniformly at random graph of…
Spanning trees in random series-parallel graphs
Julia Ehrenmüller, Juanjo Rué
By means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on vertices chosen uniformly at random satisfie…
Many 2-level polytopes from matroids
Francesco Grande, Juanjo Rué
The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-level matroids…
On the limiting distribution of the metric dimension for random forests
Dieter Mitsche, Juanjo Rué
The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. I…
Analytic combinatorics of chord and hyperchord diagrams with crossings
Vincent Pilaud, Juanjo Rué
Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of cro…
Threshold functions and Poisson convergence for systems of equations in random sets
Juanjo Rué, Christoph Spiegel, Ana Zumalacárregui
We present a unified framework to study threshold functions for the existence of solutions to linear systems of equations in random sets which includes arithmetic progressions, sum…
Dynamic Programming for Graphs on Surfaces
Juanjo Rué, Ignasi Sau, Dimitrios M. Thilikos
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to g…
Asymptotic Enumeration of Non-crossing Partitions on Surfaces
Juanjo Rué, Ignasi Sau, Dimitrios M. Thilikos
We generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface and introduce the number of non-crossin…
On polynomial representation functions for multilinear forms
Juanjo Rué
Given an infinite sequence of positive integers $\cA$, we prove that for every nonnegative integer the number of solutions of the equation , $a_1,\,..., a_k\in \…
Asymptotic study of subcritical graph classes
Michael Drmota, Éric Fusy, Mihyun Kang +2
We present a unified general method for the asymptotic study of graphs from the so-called "subcritical" graph classes, which include the classes of cacti graphs, outerplanar gra…
Graph classes with given 3-connected components: asymptotic enumeration and random graphs
Omer Gimenez, Marc Noy, Juanjo Rue
Consider a family of 3-connected graphs of moderate growth, and let be the class of graphs whose 3-connected components are graphs in . We…
Enumerating simplicial decompositions of surfaces with boundaries
Olivier Bernardi, Juanjo Rué
It is well-known that the triangulations of the disc with vertices on its boundary are counted by the th Catalan number . This paper deal…