MD - Matemàtica Discreta
http://hdl.handle.net/2117/3546
Fri, 20 Oct 2017 13:29:40 GMT2017-10-20T13:29:40ZCounting outerplanar maps
http://hdl.handle.net/2117/108706
Counting outerplanar maps
Geffner, I.; Noy Serrano, Marcos
A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice paths. As a consequence of our
results, we obtain an e cient scheme for encoding simple outerplanar maps.
Mon, 16 Oct 2017 08:23:36 GMThttp://hdl.handle.net/2117/1087062017-10-16T08:23:36ZGeffner, I.Noy Serrano, MarcosA map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice paths. As a consequence of our
results, we obtain an e cient scheme for encoding simple outerplanar maps.Subgraph statistics in subcritical graph classes
http://hdl.handle.net/2117/108598
Subgraph statistics in subcritical graph classes
Drmota, Michael; Ramos Garrido, Lander; Rué Perna, Juan José
Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series-parallel graphs.
Tue, 10 Oct 2017 13:38:22 GMThttp://hdl.handle.net/2117/1085982017-10-10T13:38:22ZDrmota, MichaelRamos Garrido, LanderRué Perna, Juan JoséLet H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and variance. The main ingredient in our proof is the analytic framework developed by Drmota, Gittenberger and Morgenbesser to deal with infinite systems of functional equations [Drmota, Gittenberger, and Morgenbesser, Submitted]. As a case study, we obtain explicit expressions for the number of triangles and cycles of length 4 in the family of series-parallel graphs.Location in maximal outerplanar graphs
http://hdl.handle.net/2117/107909
Location in maximal outerplanar graphs
Claverol Aguas, Mercè; García, Alfredo; Hernández, Gregorio; Hernando Martín, María del Carmen; Maureso Sánchez, Montserrat; Mora Giné, Mercè; Tejel, Javier
In this work we study the metric dimension and the
location-domination number of maximal outerplanar
graphs. Concretely, we determine tight upper and
lower bounds on the metric dimension and characterize
those maximal outerplanar graphs attaining the
lower bound. We also give a lower bound on the
location-domination number of maximal outerplanar
graphs.
Fri, 22 Sep 2017 11:18:42 GMThttp://hdl.handle.net/2117/1079092017-09-22T11:18:42ZClaverol Aguas, MercèGarcía, AlfredoHernández, GregorioHernando Martín, María del CarmenMaureso Sánchez, MontserratMora Giné, MercèTejel, JavierIn this work we study the metric dimension and the
location-domination number of maximal outerplanar
graphs. Concretely, we determine tight upper and
lower bounds on the metric dimension and characterize
those maximal outerplanar graphs attaining the
lower bound. We also give a lower bound on the
location-domination number of maximal outerplanar
graphs.A lower bound for the size of a Minkowski sum of dilates
http://hdl.handle.net/2117/104404
A lower bound for the size of a Minkowski sum of dilates
Hamidoune, Yayha Old; Rué Perna, Juan José
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author.
Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progression.
Mon, 15 May 2017 09:11:57 GMThttp://hdl.handle.net/2117/1044042017-05-15T09:11:57ZHamidoune, Yayha OldRué Perna, Juan JoséLet A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author.
Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progression.Asymptotic enumeration of non-crossing partitions on surfaces
http://hdl.handle.net/2117/104401
Asymptotic enumeration of non-crossing partitions on surfaces
Rué Perna, Juan José; Sau, Ignasi; Thilikos Touloupas, Dimitrios
We generalize the notion of non-crossing partition on a disk to general surfaces
with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the boundary of S
Mon, 15 May 2017 08:44:00 GMThttp://hdl.handle.net/2117/1044012017-05-15T08:44:00ZRué Perna, Juan JoséSau, IgnasiThilikos Touloupas, DimitriosWe generalize the notion of non-crossing partition on a disk to general surfaces
with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the boundary of SOuterplanar obstructions for the vertex feedback set
http://hdl.handle.net/2117/104395
Outerplanar obstructions for the vertex feedback set
Rué Perna, Juan José; Thilikos Touloupas, Dimitrios; Stavropoulos, Konstantinos
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 the set of all outerplanar graphs in obs(Fk). I
Mon, 15 May 2017 07:47:43 GMThttp://hdl.handle.net/2117/1043952017-05-15T07:47:43ZRué Perna, Juan JoséThilikos Touloupas, DimitriosStavropoulos, KonstantinosFor 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 the set of all outerplanar graphs in obs(Fk). IOn the error term of the logarithm of the lcm of quadratic sequences
http://hdl.handle.net/2117/104311
On the error term of the logarithm of the lcm of quadratic sequences
Rué Perna, Juan José; Sarka, Paulius; Zumalacárregui, Ana
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 calculate the error term for the asymptotics obtained by Cilleruelo
Thu, 11 May 2017 10:25:33 GMThttp://hdl.handle.net/2117/1043112017-05-11T10:25:33ZRué Perna, Juan JoséSarka, PauliusZumalacárregui, AnaWe 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 calculate the error term for the asymptotics obtained by CillerueloOn the number of nonzero digits of some integer sequences
http://hdl.handle.net/2117/104309
On the number of nonzero digits of some integer sequences
Cilleruelo, Javier; Luca, Florián; Rué Perna, Juan José; Zumalacárregui, Ana
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
Thu, 11 May 2017 09:55:21 GMThttp://hdl.handle.net/2117/1043092017-05-11T09:55:21ZCilleruelo, JavierLuca, FloriánRué Perna, Juan JoséZumalacárregui, AnaLet 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 sequenceAsymptotic study of subcritical graph classes
http://hdl.handle.net/2117/104308
Asymptotic study of subcritical graph classes
Drmota, Michael; Fusy, Éric; Kang, Mihyun; Kraus, Veronika; Rué Perna, Juan José
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 graphs, and series-parallel graphs. This general method works in both the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp., $g_n$) of labelled (resp., unlabelled) graphs on n vertices from a subcritical graph class ${\mathcal{G}}=\cup_n {\mathcal{G}_n}$ satisfies asymptotically the universal behavior $g_n = c \!n^{-5/2} \!\gamma^n \! (1+o(1))$ for computable constants $c,\gamma$, e.g., $\gamma\approx 9.38527$ for unlabelled series-parallel graphs, and that the number of vertices of degree k (k fixed) in a graph chosen uniformly at random from $\mathcal{G}_n$ converges (after rescaling) to a normal law as $n\to\infty$.
Thu, 11 May 2017 09:45:20 GMThttp://hdl.handle.net/2117/1043082017-05-11T09:45:20ZDrmota, MichaelFusy, ÉricKang, MihyunKraus, VeronikaRué Perna, Juan JoséWe 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 graphs, and series-parallel graphs. This general method works in both the labelled and unlabelled framework. The main results concern the asymptotic enumeration and the limit laws of properties of random graphs chosen from subcritical classes. We show that the number $g_n/n!$ (resp., $g_n$) of labelled (resp., unlabelled) graphs on n vertices from a subcritical graph class ${\mathcal{G}}=\cup_n {\mathcal{G}_n}$ satisfies asymptotically the universal behavior $g_n = c \!n^{-5/2} \!\gamma^n \! (1+o(1))$ for computable constants $c,\gamma$, e.g., $\gamma\approx 9.38527$ for unlabelled series-parallel graphs, and that the number of vertices of degree k (k fixed) in a graph chosen uniformly at random from $\mathcal{G}_n$ converges (after rescaling) to a normal law as $n\to\infty$.Dynamic programming for graphs on surfaces
http://hdl.handle.net/2117/104306
Dynamic programming for graphs on surfaces
Rué Perna, Juan José; Sau, Ignasi; Thilikos, Dimitrios
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 general families
of problems where standard dynamic programming runs in 2O(k·log k).
Our approach combines tools from topological graph theory and
analytic combinatorics.
Thu, 11 May 2017 09:30:07 GMThttp://hdl.handle.net/2117/1043062017-05-11T09:30:07ZRué Perna, Juan JoséSau, IgnasiThilikos, DimitriosWe 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 general families
of problems where standard dynamic programming runs in 2O(k·log k).
Our approach combines tools from topological graph theory and
analytic combinatorics.