arXiv subjects

Lander Ramos

Publications and source records attributed to Lander Ramos.

4 recordsLinked to original sources

arXiv2019

Maximal independent sets and maximal matchings in series-parallel and related graph classes

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 satisfy a proper sub-criticality condition. In particular we cover trees, cacti graphs and series-parallel graphs. The proof methods are based on a generating function approach and a proper singularity analysis of solutions of implicit systems of functional equations in several variables. As a byproduct, this method extends previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988].

math.CO↗

arXiv2015

Subgraph statistics in subcritical graph classes

Let $H$ be a fixed graph and $\mathcal{G}$ a subcritical graph class. In this paper we show that the number of occurrences of $H$ (as a subgraph) in a uniformly at random graph of size $n$ in $\mathcal{G}$ 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. As a case study, we get explicit expressions for the number of triangles and cycles of length four for the family of series-parallel graphs.

math.CO↗

arXiv2015

Graphs with degree constraints

Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs with a given minimum degree, and establishes new ones, such as the enumeration of Euler graphs, i.e. where all vertices have an even degree. Those results are derived using analytic combinatorics.

math.CO↗

arXiv2014

Random planar maps and graphs with minimum degree two and three

We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to the core of a random planar graph is of order c log(n) for an explicit constant c. These results provide new information on the structure of random planar graphs.

math.CO↗