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Graph polynomials and group coloring of graphs
(2022-05-01)
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Article.
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Let A be an Abelian group and let G be a simple graph. We say that G is A-colorable if, for some fixed orientation of G and every edge labeling l:E(G)¿A, there exists a vertex coloring c by the elements of A such that ...
On the optimality of the uniform random strategy
(2018-01-01)
Article.
Accés restringit per política de l'editorial
Article.
Accés restringit per política de l'editorial
Biased Maker-Breaker games, introduced by Chvátal and Erdos, are central to the field of positional games and have deep connections to the theory of random structures. The main questions are to determine the smallest bias ...
On the treewidth and related parameters of random geometric graphs
(2017-06-22)
Article.
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Article.
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We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ¿ G(n, r) in [0, v n] 2 . More precisely, let rc denote the threshold radius for the appearance of the giant component in G(n, r). ...
Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes
(Springer, 2022-12-31)
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Article.
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We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered ...
Further results on random cubic planar graphs
(2020-06)
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Article.
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We 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 ...
Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal
(Institute of Electrical and Electronics Engineers (IEEE), 2022-02-09)
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Article.
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We prove that there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n¿q2 over Fq2 if and only if there is a polynomial g¿Fq2 of degree at most (q-k)q-1 such that g+gq has ...
Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups
(2020-04-01)
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Article.
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The classical result by Dyer–Scott about fixed subgroups of finite order automor-phisms of Fnbeing free factors of Fn is no longer true inZm×Fn. Within this more generalcontext, we prove a relaxed version in the spirit of ...
Diameter and stationary distribution of random r-out digraphs
(2020-08-07)
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Article.
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Let D(n, r) be a random r-out 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 ...
A list of applications of stallings automata
(2022-11-22)
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Article.
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This survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. ...
Autòmats de Stallings, un camí d'anada i tornada
(2022-12-14)
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Article.
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En aquest article revisem algunes de les propietats fonamentals del grup lliure i fem una exposició detallada de la teoria dels autòmats de Stallings, una interpretació geomètrica dels seus subgrups que ha estat (i segueix ...