**Recent papers**

- Counting outerplanar maps (with Ivan Geffner) Electr. J. Combinat. 2017.
- Limit laws for minor-closed classes of graphs (with Peter Heinig, Tobias Muller and Anusch Taraz), to appear in
*J. Combin. Theory Ser. B*PDF. We establish zero-one laws and convergence laws for several minor-closed classes of graphs, both in first order and monadic second order logic. A main result is the existence of an MSO convergence law for every addable minor-closed class. - Maximum degree in minor-closed classes of graphs (with Omer Giménez and Dieter Mitsche) Europ. J. Combinat. 2016 PDF. Given a class of graphs G closed under taking minors, we study the maximum degree of random graphs from G under the uniform distribution. We prove several lower and upper bounds that hold with high probability.
- Graph enumeration PDF. Chapter 6 from the Handbook of Enumerative combinatorics, edited by Miklós Bóna (CRC Press 2015).
- On the diameter of random planar graphs (with Guillaume Chapuy, Éric Fusy and Omer Giménez) Combinat. Probab. Comput. 2015 PDF. We show that the diameter of a random planar graph with n vertices is of order n^(1/4+o(1)).
- The probability of planarity of a random graph near the critical point (with Vlady Ravelomanana and Juajo Rué)
*Proc. AMS*2015 PDF. We give an answer to an old question of Erdos and Renyi on the probability of a random graph with n vertices and n/2 edges being planar.

**Selected past papers**

- Random planar graphs and beyond, in
*Proc. ICM*2014 PDF. A survey of random planar graphs, graphs on surfaces, and graphs from minor-closed classes. - The maximum degree of random planar graphs (with Michael Drmota, Omer Giménez, Kosta Panagiotou and Angelika Steger)
*Proc. London Math. Soc.*2014 PDF. We show that the maximum degree of a random planar graph with n vertices is concentrated around c log(n) for some explcit constant c. Previously McDiarmid and Reed (2008) had shown that it is θ(log n). - Extremal statistics on non-crossing configurations (with Michael Drmota and Anna de Mier)
*Discrete Math.*2014 PDF. We show that the maximum vertex degree and the size of the largest component in various random non-crossing configurations is of order log(n), and the diameter is of order √n. - On the number of self-dual rooted maps (with Sergey Kitaev and Anna de Mier)
*European J. Combin.*2014 PDF. We show that the number of self-dual rooted maps with n edges is 3^n*C(n), where C(n) is a Catalan number. We also determine the number of 2- and 3-connected self-dual rooted maps. - Graph classes with given 3-connected components (with Omer Giménez and Juanjo Rué)
*Random Structures Algorithms*2013 PDF. A general framework based on singularity analyis is presented for analyzing classes of graphs defined in terms of their 3-connected members. This scheme includes planar, series-parallel and related classes. - Evaluation of the Tutte polynomial at the points (1,−1) and (2,−1) (with Andrew Goodall, Criel Merino and Anna de Mier)
*Ann. Comb.*2013 PDF. Motivated by the identity t(Kn+2; 1,−1) = t(Kn; 2, −1), where t(G; x, y) is the Tutte polynomial of a graph G, we search for graphs G having the property that there is a pair of vertices u, v such that t(G; 1, −1) = t(G− {u, v}; 2, −1). - Clusters, generating functions and asymptotics for consecutive patterns in permutations (with Sergi Elizalde) Adv. Appl. Math 2012 PDF
- On the maximum number of cycles in outerplanar and series-parallel graphs (with Anna de Mier) Graphs Combin. 2012 PDF
- The maximum degree of series-parallel graphs (with Michael Drmota and Omer Giménez)
*Combin. Probab. Comput.*2011 PDF - Degree distribution in random planar graphs (with Michael Drmota and Omer Giménez)
*J. Combin. Theory Ser. A*2011 PDF - Asymptotic enumeration and limit laws for graphs of fixed genus (with Guillaume Chapuy, Éric Fusy, Omer Giménez, and Bojan Mohar, Bojan)
*J. Combin. Theory Ser. A*2011 PDF - Growth constants of minor-closed classes of graphs (with Olivier Bernardi and Dominic Welsh)
*J. Combin. Thery Ser. B*2010 PDF - Vertices of Given Degree in Series-Parallel Graphs (with Michael Drmota and Omer Giménez) Random Structures Algorithms 2010 PDF
- Asymptotic enumeration and limit laws for planar graphs (with Omer Giménez)
*Journal AMS*2009 PDF - Counting planar graphs and related families of graphs (with Omer Giménez) in
*Surveys in Combinatorics*2009 PDF. - Asymptotic enumeration and limit laws of series-parallel graphs (with Manuel Bodirsky, Omer Giménez and Mihyun Kang)
*European J. Combin*. 2007 PDF - Computing Tutte polynomials of graphs with bounded clique-width (with Omer Giménez and Petr Hlineny)
*SIAM J. Discrete Math.*2006 PDF - A solution to the tennis ball problem (with Anna de Mier)
*Theoret. Comput. Sci.*2005 PDF - Lattice Path Matroids: enumerative aspects and Tutte polynomials (with Joseph Bonin and Anna de Mier).
*J. Combin. Theory Ser. A*2003 PDF - Graphs determined by polynomial invariants.
*Theoret. Comput. Sci.*2003 PDF - Irreducibility of the Tutte polynomial of a connected matroid (with Criel Merino and Anna de Mier).
*J. Combin. Theory Ser. B*2001 PDF - Lower bounds on the number of crossing-free graphs of K_n (with Alfredo García and Javier Tejel).
*Comput. Geometry: Theory Applic.*2000 PDF - Analytic Combinatorics of non-Crossing Configurations (with Philippe Flajolet)
*Discrete**Math.*1999 PDF - Flipping edges in triangulations (with Ferran Hurtado and Jorge Urrutia).
*Discrete Comput. Geometry*1999 PDF - Graph of triangulations of a convex polygon and tree of triangulations (with Ferran Hurtado).
*Comput. Geometry: Theory Applic.*1999 PDF

- Enumeration of non-crossing trees on a circle.
*Discrete Math*1998 PDF