Browsing by Author "Rué Perna, Juan José"

Isolated cycles of critical random graphs
Noy Serrano, Marcos; Rasendrahasina, Vonjy; Ravelomanana, Vlady; Rué Perna, Juan José (Society for Industrial and Applied Mathematics (SIAM), 2017)
Conference report
Open AccessConsider the ErdosRenyi random graph G(n, M) built with n vertices and M edges uniformly randomly chosen from the set of n2 edges. Let L be a set of positive integers. For any number of edges M 6n/2 + O(n 2/3 ), we compute ... 
Los números trascendentes
Fresán, Javier; Rué Perna, Juan José (Ediciones La Catarata, 201305)
Book
Restricted access  publisher's policyLa expresión e¿ v163 es mucho más que la suma de sus partes e, ¿ y v163. Lejos de ser una elección casual, esta fórmula sirve a los autores de hilo conductor para adentrase en las áreas de la investigación más activa de ... 
Many 2level polytopes from matroids
Grande, Francesco; Rué Perna, Juan José (20151026)
Article
Open AccessThe family of 2level matroids, that is, matroids whose base polytope is 2level, has been recently studied and characterized by means of combinatorial properties. 2Level matroids generalize seriesparallel graphs, which ... 
Matemáticas y redes
Rué Perna, Juan José; Zumalacárregui, Ana (20140101)
Part of book or chapter of book
Open Access 
Maximal independent sets and maximal matchings in seriesparallel and related graph classes
Drmota, Michael; Ramos, Lander; Requilé, Clément; Rué Perna, Juan José (Schloss Dagstuhl  LeibnizZentrum für Informatik, 2018)
Conference lecture
Open AccessWe provide combinatorial decompositions as well as asymptotic tight estimates for two maximal parameters: the number and average size of maximal independent sets and maximal matchings in seriesparallel graphs (and related ... 
Memorial to Javier Cilleruelo: A Problem list
Candela, Pablo; Rué Perna, Juan José; Serra Albó, Oriol (20180323)
Article
Open AccessThis is a list of problems in combinatorial number theory gathered on the occasion of the meeting The Music of Numbers to honor the memory of the late Javier Cilleruelo (19612016). 
On a problem of Sárközy and Sós for multivariate linear forms
Rué Perna, Juan José; Spiegel, Christoph (20180701)
Article
Restricted access  publisher's policyWe prove that for pairwise coprime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes ... 
On a question of Sárkozy and Sós for bilinear forms
Cilleruelo, Javier; Rué Perna, Juan José (20090202)
Article
Restricted access  publisher's policyWe prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers such that the representation function r(n)=#{(a, a'): n=$k{_1}a$ + $k{_2}a'$, a,a' ∊ $\emph{A}$} is constant for n large ... 
On polynomial representation functions for multivariate linear forms
Rué Perna, Juan José (20131101)
Article
Open AccessGiven an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 +· · ·+ak, a1, . . . , ak ¿ A, is not constant for n large enough. This result ... 
On the error term of the logarithm of the lcm of quadratic sequences
Rué Perna, Juan José; Sarka, Paulius; Zumalacárregui, Ana (20130109)
Article
Open AccessWe study the logarithm of the least common multiple of the sequence of integers given by 12 + 1, 2 2 + 1, . . . , n2 + 1. Using a result of Homma [4] on the distribution of roots of quadratic polynomials modulo primes we ... 
On the fractional Parts of a^n/n
Cilleruelo, Javier; Luca, Florian; Kumchev, Angel; Rué Perna, Juan José; Shparlinski, Igor (20130930)
Article
Open AccessWe give various results about the distribution of the sequence {a n/n}n=1 modulo 1, where a = 2 is a fixed integer. In particular, we find and infinite subsequence A such that {a n/n}n¿A is well distributed. Also we show ... 
On the limiting distribution of the metric dimension for random forests
Rué Perna, Juan José; Mitsche, Dieter (20150320)
Article
Open AccessThe 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. In this paper we investigate the metric ... 
On the number of nonzero digits of some integer sequences
Cilleruelo, Javier; Luca, Florián; Rué Perna, Juan José; Zumalacárregui, Ana (20120605)
Article
Open AccessLet b = 2 be a fixed positive integer. We show for a wide variety of sequences {an}8n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence 
On the optimality of the uniform random strategy
kush, Christopher; Rué Perna, Juan José; Spiegel, Christoph; Szabó, T. (20180101)
Article
Restricted access  publisher's policyBiased MakerBreaker games, introduced by Chvátal and Erdos, are central to the field of positional games and have deep connections to the theory of random structures. The main questions are to determine the smallest bias ... 
Outerplanar obstructions for the vertex feedback set
Rué Perna, Juan José; Thilikos Touloupas, Dimitrios; Stavropoulos, Konstantinos (20120702)
Article
Open AccessFor k = 1, let Fk be the class of graphs that contains k vertices meeting all its cycles. The minorobstruction set for Fk is the set obs(Fk) containing all minorminimal graphs that do not belong to Fk. We denote by Yk ... 
Pentagonal chains and annuli as models for designing nanostructures from cages
Rosenfeld, Vladimir; Dubrynin, Andrey; Oliva, Josep Ma; Rué Perna, Juan José (20160301)
Article
Open AccessCarbon is the most versatile of chemical elements in combining with itself or other elements to form chains, rings, sheets, cages, and periodic 3D structures. One of the perspective trends for creating new molecules of ... 
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 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 strategies are nearly optimal for generalized van der Waerden Games
Kusch, C.; Rué Perna, Juan José; Spiegel, Christoph; Szabó, T. (20170801)
Article
Restricted access  publisher's policyIn a (1 : q) MakerBreaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ... 
Spanning trees in random seriesparallel graphs
Rué Perna, Juan José; Ehrenmüller, Julia (20160401)
Article
Open AccessBy means of analytic techniques we show that the expected number of spanning trees in a connected labelled seriesparallel graph on n vertices chosen uniformly at random satisfies an estimate of the form s%n(1 + o(1)), ...