School of Mathematics, University of Birmingham. Office 215A, Watson Building (R15) Email: g.perarnau at bham.ac.uk Tel: +44 (0) 121 414 2619 (Last updated: Jan, 2016)

I did my degree in Mathematics and a master in Applied Mathematics in the FME (Universitat Politècnica de Catalunya, UPC). In 2013 I defended my PhD Thesis at COMBGRAPH (UPC) under the supervision of Oriol Serra. I had the opportunity to be a CARP Postdoc Fellow at School of Computer Science, at Mcgill University, where I enjoyed my days working with Bruce Reed and Louigi AddarioBerry. After a short period as a Research Fellow, in January 2016 I became a Lecturer in the School of Mathematics at the University of Birmingham.
My main interests are in Probabilistic and Extremal Combinatorics, Random Combinatorial Structures and the analysis of Randomized Algorithms.
RESEARCH
Journal Publications
Forthcoming
 M. Coulson and G. Perarnau. A Rainbow Dirac theorem. Submitted. Preprint.
 G. Chapuy and G. Perarnau. On the number of coloured triangulations of dmanifolds. Submitted. Preprint.
 M. Delcourt, G. Perarnau and L. Postle. Rapid mixing of Glauber dynamics for colorings below Vigoda's 11/6 threshold. Submitted. Preprint.
 M. Coulson, P. Keevash, G. Perarnau and L. Yepremyan. Rainbow factors in hypergraphs. Submitted. Preprint.
 N. Fountoulakis, F. Joos and G. Perarnau. Percolation on random graphs with a fixed degree sequence. Submitted. Preprint.
 L. AddarioBerry, B. Balle and G. Perarnau. Diameter and Stationary Distribution of Random rout Digraphs. Submitted. Preprint.
Published
 G. Chapuy and G. Perarnau. Local convergence and stability of tight bridgeaddable graph classes. To appear in Canadian Journal of Mathematics. Preprint.
 G. Chapuy and G. Perarnau. Connectivity in bridgeaddable graph classes: the McDiarmidStegerWelsh conjecture. To appear in Journal of Combinatorial Theory, Series B. Preprint.
 M. Coulson and G. Perarnau. Rainbow matchings in Dirac bipartite graphs. To appear in Random Structures & Algorithms.Preprint.
 G. Perarnau and W. Perkins. Counting independent sets in cubic graphs of given girth. Journal of Combinatorial Theory, Series B, 133 211242, 2018. Preprint.
 F. Joos and G. Perarnau. Critical percolation on random regular graphs. Proc. of the AMS 146,33213332, 2018. Preprint.
 F. Joos, G. Perarnau, D. Rautenbach and B. Reed. How to determine if a random graph with a fixed degree sequence has a giant component. Probability Theory and Related Fields, 170(1), 263310, 2018. Preprint.
 G. Perarnau and B. Reed. Existence of spanning Ffree subgraphs with large minimum degree. Combinatorics, Probability and Computing, 26(3):448–467, 2017. Preprint.
 D. Mitsche and G. Perarnau. On the treewidth and related parameters of random geometric graphs. SIAM J. Discrete Math., 31(2):1328–1354, 2017.
 X.S. Cai, G. Perarnau, B. Reed and A.B. Watts. Acyclic edge colourings of graphs with large girth. Random Structures & Algorithms, 50, 511–533, 2017. Preprint.
 F. Foucaud, G. Perarnau and O. Serra. Random subgraphs make identification affordable. Journal of Combinatorics, 8(1):57–77, 2017. Preprint.
 G. Perarnau and O. Serra. Correlation among runners and some results on the Lonely Runner Conjecture. Electronic Journal of Combinatorics 23(1):P1.50, 2016. Preprint.
 J. Diaz, D. Mitsche, G. Perarnau and X. PérezGiménez. On the relation between graph distance and Euclidean distance in random geometric graphs. Advances in Applied Probability 48.3, September 2016. Preprint.
 N. Bousquet and G. Perarnau. Fast Recoloring of Sparse Graphs. European Journal of Combinatorics, 52(A):111, 2016. Preprint.
 F. Foucaud, M. Krivelevich and G. Perarnau. Large subgraphs without short cycles. SIAM Journal of Discrete Mathematics, 29(1):6578, 2015. Preprint.
 R. Kang and G. Perarnau. Decomposition of bounded degree graphs into C_{4}free subgraphs, European Journal of Combinatorics, 44(A):99105, 2015. Preprint.
 A. Abiad, M.A. Fiol, W.H. Haemers and G. Perarnau. An interlacing approach for bounding the sum of laplacian eigenvalues of graphs, Linear Algebra and its Applications, 448:11–21, 2014. Preprint.
 G. Perarnau and O. Serra. On the treedepth of random graphs, Discrete Applied Mathematics, 168:119126, 2014. Preprint.
 G. Perarnau and O. Serra. Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting, Combinatorics, Probability and Computing, 22(5):783799, 2013. Preprint.
 G. Perarnau. A probabilistic approach to consecutive pattern avoiding in permutations, Journal of Combinatorial Theory, Series A, 120(5):9981011, 2013. Preprint.
 G. Perarnau and G. Petridis. Matchings in Random Biregular Bipartite Graphs, The Electronic Journal of Combinatorics 20(1):P60, 2013. Preprint.
 F. Foucaud, I. Honkala, T. Laihonen, A. Parreau and G. Perarnau. Locally identifying colourings for graphs with given maximum degree, Discrete Mathematics, 312(10):18321837, 2012. Preprint.
 F. Foucaud and G. Perarnau. Bounds for identifying codes in terms of degree parameters, The Electronic Journal of Combinatorics 19(1):P32, 2012. Preprint.
Refereed Conference Publications
 F. Joos, G. Perarnau, D. Rautenbach and B. Reed. How to determine if a random graph with a fixed degree sequence has a giant component. FOCS 2016.
 G. Chapuy and G. Perarnau. Local convergence and stability of tight bridgeaddable graph classes. APPROXRANDOM 2016.
 G. Chapuy and G. Perarnau. Connectivity in bridgeaddable graph classes: the McDiarmidStegerWelsh conjecture. SODA 2016.
 F. Foucaud, G. Perarnau and O. Serra. Random subgraphs make identification affordable. EUROCOMB 2013.
 A. Abiad, M.A. Fiol, W.H. Haemers and G. Perarnau. An interlacing approach for bounding the sum of laplacian eigenvalues of graphs. EUROCOMB 2013.
 D. Mitsche and G. Perarnau. On the treewidth and related parameters of random geometric graphs. STACS 2012.
 G. Perarnau and O. Serra. Rainbow matchings: existence and counting. EUROCOMB 2011.
 A. Padrol, G. Perarnau, J. Pfeifle and V. MuntésMulero. Overlapping Community Search for social networks. ICDE 2010.
Selected talks
 Connectivity in bridgeaddable graph classes: the McDiarmidStegerWelsh conjecture, RSA 2015, Pittsburgh (July 2015).
 Acyclic edge colorings of graphs with large girth, BMD 2014, Barcelona (October 2014).
 Spanning Ffree subgraphs with large minimum degree, SIAM Conference in DM 2014, Minneapolis (June 2014).
 A probabilistic approach to consecutive pattern avoiding in permutations, VIII JMDA, Almeria (July 2012).
 Rainbow Matchings: existence and counting, EUROCOMB 2011, Budapest (September 2011).