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
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Articles de revista [13]
Recent Submissions

Structure and enumeration of K4minorfree links and linkdiagrams
(20201001)
Article
Open AccessWe study the class of linktypes that admit a minorfree diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of . We prove that is the closure of a subclass of ... 
On the number of coloured triangulations of dmanifolds
(20200311)
Article
Open AccessWe give superexponential lower and upper bounds on the number of coloured ddimensional triangulations whose underlying space is an oriented manifold, when the number of simplices goes to infinity and d=3 is fixed. In the ... 
On varieties defined by large sets of quadrics and their application to errorcorrecting codes
(20201001)
Article
Restricted access  publisher's policyLet U be a ( k1 2  1)dimensional subspace of quadratic forms defined on F k with the property that U does not contain any reducible quadratic form. Let V (U) be the points of PG(k  1, F) which are zeros of all quadratic ... 
The Glauber dynamics for edgecolorings of trees
(20200926)
Article
Restricted access  publisher's policyLet T be a tree on n vertices and with maximum degree ¿. We show that for k = ¿ + 1 the Glauber dynamics for kedgecolourings of T mixes in polynomial time in n. The bound on the number of colours is best possible as the ... 
Sidon set systems
(20200211)
Article
Open AccessA family A of ksubsets of {1,2,…,N} is a Sidon system if the sumsets A+B, A,B¿A are pairwise distinct. We show that the largest cardinality Fk(N) of a Sidon system of ksubsets of [N] satisfies Fk(N)=(N1k1)+Nk and the ... 
A step beyond Freiman’s theorem for set addition modulo a prime
(20200101)
Article
Open AccessFreiman’s 2.4Theorem states that any set A¿Zp satisfying 2A=2.4A3 and A<p/35 can be covered by an arithmetic progression of length at most 2AA+1. A more general result of Green and Ruzsa implies that this ... 
On the smallest trees with the same restricted Upolynomial and the rooted Upolynomial
(20210301)
Article
Open AccessIn this article, we construct explicit examples of pairs of nonisomorphic trees with the same restricted U polynomial for every k; by this we mean that the polynomials agree on terms with degree at most k + 1. The main ... 
Diameter and stationary distribution of random rout digraphs
(20200807)
Article
Open AccessLet D(n, r) be a random rout regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r = 2, there exists ¿r > 0 such that diam(D(n, r)) = (1 + ¿r + o(1)) logr n. The ... 
On list kcoloring convex bipartite graphs
(Springer, 2020)
Conference report
Restricted access  publisher's policyList k–Coloring (LI kCOL) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in {1,2,..., k}. The problem is known to be NPhard ... 
A rainbow Dirac's theorem
(20200101)
Article
Open AccessA famous theorem of Dirac states that any graph on n vertices with minimum degree at least n/2 has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton ... 
Enumeration of labelled 4regular planar graphs
(20190801)
Article
Open AccessWe present the first combinatorial scheme for counting labelled 4regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function of labelled 4regular ... 
Further results on random cubic planar graphs
(202006)
Article
Restricted access  publisher's policyWe provide precise asymptotic estimates for the number of several classes of labeled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by ...