GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

 

The research of the group focuses on interrelated aspects of combinatorics: Graph theory, Random Graphs, Probabilistic method, Geometric group theory and algebraic methods, Enumerative combinatorics, Combinatorial geometry, and Combinatorial number theory. Some recent research achievements are: Proof of the Maximum Distance Separable codes conjecture for prime fields; solution of a conjecture of Green on the removal lemma for systems of equations in finite fields

Recent Submissions

  • The central tree property and algorithmic problems on subgroups of free groups 

    Roy, Mallika; Ventura Capell, Enric; Weil, Pascal (De Gruyter, 2024-02-14)
    Article
    Open Access
    We study the average case complexity of the Uniform Membership Problem for subgroups of free groups, and we show that it is orders of magnitude smaller than the worst case complexity of the best known algorithms. This ...

  • On minimum vertex bisection of random d-regular graphs 

    Díaz Cort, Josep; Yasar Diner, Oznur; Serna Iglesias, María José; Serra Albó, Oriol (2024-09)
    Article
    Open Access
    Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the ...

  • Short synchronizing words for random automata 

    Chapuy, Guillaume; Perarnau Llobet, Guillem (Curran Associates, Inc., 2023)
    Conference report
    Open Access
    We prove that a uniformly random automaton with n states on a 2-letter alphabet has a synchronizing word of length with high probability (w.h.p.). That is to say, w.h.p. there exists a word ¿ of such length, and a state ...

  • Percolation on dense random graphs with given degrees 

    Lichev, Lyuben; Mitsche, Dieter; Perarnau Llobet, Guillem (Elsevier, 2024-03-26)
    Article
    Open Access
    In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond ...

  • Block statistics in subcritical graph classes 

    Ralaivaosaona, Dimbinaina; Requile, Clement; Wagner, Stephan (2020)
    Conference report
    Open Access
    We study block statistics in subcritical graph classes; these are statistics that can be defined as the sum of a certain weight function over all blocks. Examples include the number of edges, the number of blocks, and the ...

  • Chordal graphs with bounded tree-width 

    Castellví, Jordi; Drmota, Michael; Noy Serrano, Marcos; Requile, Clement (2024-06)
    Article
    Open Access
    Given t \geq 2 and 0 \leq k \leq t, we prove that the number of labelled k-connected chordal graphs with n vertices and tree-width at most t is asymptotically cn -5/2 \gamma {n} n!, as n \to \infty, for some constants c, ...

  • Proper colouring Painter–Builder game 

    Bednarska-Bzdega, Malgorzata; Krivelevich, Michael; Mészáros, Viola; Requile, Clement (2018-03)
    Article
    Open Access
    We consider the following two-player game, parametrised by positive integers and . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph ...

  • Largest component of subcritical random graphs with given degree sequence 

    Coulson, Matthew John; Perarnau Llobet, Guillem (Project Euclid, 2023-02)
    Article
    Open Access
    We study the size of the largest component of two models of random graphs with prescribed degree sequence, the configuration model (CM) and the uniform model (UM), in the (barely) subcritical regime. For the CM, we give ...

  • Variants of plane diameter completion 

    Golovach, Petr; Requile, Clement; Thilikos, Dimitrios M. (2015-11-19)
    Article
    Open Access
    The Plane Diameter Completion problem asks, given a plane graph G and a positive integer d, if it is a spanning subgraph of a plane graph H that has diameter at most d. We examine two variants of this problem where the ...

  • Enumeration of rooted 3-connected bipartite planar maps 

    Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2024-03-07)
    Article
    Open Access
    We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, ...

  • Rankings in directed configuration models with heavy tailed in-degrees 

    Cai, Xing Shi; Caputo, Pietro; Perarnau Llobet, Guillem; Quattropani, Matteo (2023-12-01)
    Article
    Open Access
    We consider the extremal values of the stationary distribution of sparse directed random graphs with given degree sequences and their relation to the extremal values of the in-degree sequence. The graphs are generated by ...

  • Homomorphisms between graphs embedded in surfaces 

    Garijo Royo, Delia; Goodall, Andrew; Vena Cros, Lluís (Elsevier, 2024-05)
    Article
    Open Access
    We extend the notion of graph homomorphism to cellularly embedded graphs (maps) by designing operations on vertices and edges that respect the surface topology; we thus obtain the first definition of map homomorphism that ...

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