Now showing items 21-40 of 45

• #### Isolated cycles of critical random graphs ﻿

(Society for Industrial and Applied Mathematics (SIAM), 2017)
Conference report
Open Access
Consider the Erdos-Renyi 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 ﻿

(Ediciones La Catarata, 2013-05)
Book
Restricted access - publisher's policy
La 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 2-level polytopes from matroids ﻿

(2015-10-26)
Article
Open Access
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 generalize series-parallel graphs, which ...
• #### Matemáticas y redes ﻿

(2014-01-01)
Part of book or chapter of book
Open Access
• #### Maximal independent sets and maximal matchings in series-parallel and related graph classes ﻿

(Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
Conference lecture
Open Access
We 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 ﻿

(2018-03-23)
Article
Open Access
This 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 (1961-2016).
• #### On a problem of Sárközy and Sós for multivariate linear forms ﻿

(2018-07-01)
Article
Restricted access - publisher's policy
We prove that for pairwise co-prime 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 ﻿

(2009-02-02)
Article
Restricted access - publisher's policy
We 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 ﻿

(2013-11-01)
Article
Open Access
Given 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 ﻿

(2013-01-09)
Article
Open Access
We 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 ﻿

(2013-09-30)
Article
Open Access
We 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 ﻿

(2015-03-20)
Article
Open Access
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. In this paper we investigate the metric ...
• #### On the number of nonzero digits of some integer sequences ﻿

(2012-06-05)
Article
Open Access
Let 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 ﻿

(2018-01-01)
Article
Restricted access - publisher's policy
Biased Maker-Breaker 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 ﻿

(2012-07-02)
Article
Open Access
For k = 1, let Fk be the class of graphs that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk ...
• #### Pentagonal chains and annuli as models for designing nanostructures from cages ﻿

(2016-03-01)
Article
Open Access
Carbon 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 ﻿

(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 graphs revisited ﻿

(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 strategies are nearly optimal for generalized van der Waerden Games ﻿

(2017-08-01)
Article
Restricted access - publisher's policy
In a (1 : q) Maker-Breaker 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 series-parallel graphs ﻿

(2016-04-01)
Article
Open Access
By means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on n vertices chosen uniformly at random satisfies an estimate of the form s%-n(1 + o(1)), ...