Interesting Links

Departament de Matemàtica Aplicada
Universitat Politècnica de Catalunya.

Despatx 428. Edifici Omega. Campus Nord
C/ Jordi Girona 1-3
08034 Barcelona, Spain

Email: guillem.perarnau at upc.edu

 

 

I did my bachelor, master and PhD at Universitat Politècnica de Catalunya (UPC), advised by Oriol Serra. From 2013 to 2015 I had the pleasure to be a CARP Postdoc Fellow at McGill University, working with Bruce Reed and Louigi Addario-Berry. From 2016 to 2019 I was a Lecturer in the Combinatorics, Probability and Algorithms group at the University of Birmingham. Since 2019 I am an Associate Professor in GAPCOMB at UPC. I am affiliated to CRM and to IMTech, and to BGSMath.

My main research interests are in Probabilistic and Extremal Combinatorics, Random Combinatorial Structures, Discrete Stochastical Processes and the analysis of Randomized Algorithms.

Currently, I'm coPI of the COCOA grant, coordinator and coordinator of the Spanish Discrete and Algorithmic Mathematics Network and I participate in the RandNET MSCA Exchange Programme.

RESEARCH

Journal Publications

Preprints

Published

  • G. Chapuy and G. Perarnau. Short Synchronizing Words for Random Automata. To appear in ACM Trans. Algorithms .Preprint.
  • G. Perarnau, O. Serra. The Lonely Runner Conjecture turns 60. Computer Science Review, 58:100798, 2025. Preprint.
  • G. Chapuy and G. Perarnau. A telescopic proof of Cayley's formula theorem. American Mathematical Monthly 131(10):899--902, 2024. Preprint.
  • L. Lichev, D. Mitsche and G. Perarnau. Percolation on dense random graphs with given degrees. Journal of Combinatorial Theory, Series B, 167:250--282, 2024. Preprint.
  • A. Espuny-Díaz, P. Morris, G. Perarnau and O. Serra. Speeding up random walk mixing by starting from a uniform vertex. Electronic Journal of Probability, 29(P26):1-25, 2024. Preprint.
  • X. S. Cai, P. Caputo, G. Perarnau and M. Quattropani. Rankings in directed configuration models with heavy tailed in-degrees. Annals of Applied Probability, 33(6B):5613--5667, 2023. Preprint.
  • M. Coulson and G. Perarnau. Largest component of subcritical random graphs with given degree sequence. Electronic Journal Probability. 28:1-28, 2023. Preprint.
  • X. S. Cai and G. Perarnau. The giant component of the directed configuration model revisited. Annales IHP. Probabilites et Statistiques 59(1):244--270, 2023. Preprint.
  • X. S. Cai and G. Perarnau. The diameter of the directed configuration model. ALEA, Lat. Am. J. Probab. Math. Stat. 18:1517-1528, 2021. Preprint.
  • N. Fountoulakis, F. Joos and G. Perarnau. Percolation on random graphs with a fixed degree sequence. SIAM Journal on Discrete Mathematics, 36(1):1-46, 2022.. Preprint.
  • L. Dubois, G. Joret, G. Perarnau, M. Pilipczuk and F. Pitois. Two lower bounds for p-centered colorings. Discrete Mathematics & Theoretical Computer Science, 22:4, 2020. Preprint.
  • M. Bonamy, N. Bousquet and G. Perarnau. Frozen (Δ+1)-colourings of bounded degree graphs. Combinatorics, Probability and Computing, 30(3):330-343, 2020. Preprint.
  • M. Delcourt, M. Heinrich and G. Perarnau. The Glauber dynamics for edges colourings of trees. Random Structures & Algorithms 57(4):1050-1076, 2020.
    • Preprint.
  • M. Coulson and G. Perarnau. A Rainbow Dirac theorem. SIAM Journal of Discrete Mathematics 34(3):1670-1692, 2020. Preprint.
  • L. Addario-Berry, B. Balle and G. Perarnau. Diameter and Stationary Distribution of Random r-out Digraphs. Electronic Journal of Combinatorics 27(3) P3.28, 2020. Preprint.
  • G. Chapuy and G. Perarnau. On the number of coloured triangulations of d-manifolds. Discrete & Computational Geometry, 2020, https://doi.org/10.1007/s00454-020-00189-w. Preprint.
  • M. Coulson, P. Keevash, G. Perarnau and L. Yepremyan. Rainbow factors in hypergraphs. Journal of Combinatorial Theory, Series A 172:105184, 2020. Preprint.
  • G. Chapuy and G. Perarnau. Local convergence and stability of tight bridge-addable graph classes. Canadian Journal of Mathematics 72(3):563--601, 2020. Preprint.
  • G. Chapuy and G. Perarnau. Connectivity in bridge-addable graph classes: the McDiarmid-Steger-Welsh conjecture. Journal of Combinatorial Theory, Series B 136(C):44-71, 2019. Preprint.
  • M. Coulson and G. Perarnau. Rainbow matchings in Dirac bipartite graphs. Random Structures & Algorithms, 55(2):271-289, 2019.Preprint.
  • G. Perarnau and W. Perkins. Counting independent sets in cubic graphs of given girth. Journal of Combinatorial Theory, Series B, 133 211-242, 2018. Preprint.
  • F. Joos and G. Perarnau. Critical percolation on random regular graphs. Proc. of the AMS 146,3321-3332, 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), 263-310, 2018. Preprint.
  • G. Perarnau and B. Reed. Existence of spanning F-free 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 Journal of Discrete Mathematics, 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. Pérez-Giménez. 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):1-11, 2016. Preprint.
  • F. Foucaud, M. Krivelevich and G. Perarnau. Large subgraphs without short cycles. SIAM Journal of Discrete Mathematics, 29(1):65-78, 2015. Preprint.
  • R. Kang and G. Perarnau. Decomposition of bounded degree graphs into C4-free subgraphs, European Journal of Combinatorics, 44(A):99-105, 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 tree-depth of random graphs, Discrete Applied Mathematics, 168:119-126, 2014. Preprint.
  • G. Perarnau and O. Serra. Rainbow Perfect Matchings in Complete Bipartite Graphs: Existence and Counting, Combinatorics, Probability and Computing, 22(5):783-799, 2013. Preprint.
  • G. Perarnau. A probabilistic approach to consecutive pattern avoiding in permutations, Journal of Combinatorial Theory, Series A, 120(5):998-1011, 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):1832-1837, 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