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An analogue of Vosper's theorem for extension fields
(20171101)
Article
Open AccessWe are interested in characterising pairs S, T of Flinear subspaces in a field extension L/F such that the linear span ST of the set of products of elements of S and of elements of T has small dimension. Our central result ... 
Forbidden subgraphs in the norm graph
(20160406)
Article
Open AccessWe show that the norm graph with n vertices about View the MathML source edges, which contains no copy of the complete bipartite graph Kt,(t1)!+1, does not contain a copy of Kt+1,(t1)!1. 
On the relation between graph distance and Euclidean distance in random geometric graphs
(20160901)
Article
Open AccessGiven any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean distance and by dE(u, v) their graph distance. The problem of finding upper bounds on dG(u, v) conditional on dE(u, v) ... 
Revisiting Kneser’s theorem for field extensions
(20170531)
Article
Open AccessA Theorem of Hou, Leung and Xiang generalised Kneser’s addition Theorem to field extensions. This theorem was known to be valid only in separable extensions, and it was a conjecture of Hou that it should be valid for all ... 
Transformation and decomposition of clutters into matroids
(20170525)
Article
Open AccessA clutter is a family of mutually incomparable sets. The set of circuits of a matroid, its set of bases, and its set of hyperplanes are examples of clutters arising from matroids. In this paper we address the question of ... 
Random subgraphs make identification affordable
(20170102)
Article
Open AccessAn identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the ... 
On star forest ascending subgraph decomposition
(20170203)
Article
Open AccessThe Ascending Subgraph Decomposition (ASD) Conjecture asserts that every graph G with (n+12) edges admits an edge decomposition G=H1¿¿¿Hn such that Hi has i edges and it is isomorphic to a subgraph of Hi+1, i=1,…,n1. We ... 
Approximate results for rainbow labelings
(201703)
Article
Open AccessA simple graph G=(V,E) is said to be antimagic if there exists a bijection f:E¿[1,E] such that the sum of the values of f on edges incident to a vertex takes different values on distinct vertices. The graph G is distance ... 
Proinsulin protects against agerelated cognitive loss through antiinflammatory convergent pathways
(20170901)
Article
Open AccessBrain inflammaging is increasingly considered as contributing to agerelated cognitive loss and neurodegeneration. Despite intensive research in multiple models, no clinically effective pharmacological treatment has been ... 
(Di)graph products, labelings and related results
(201707)
Article
Open AccessGallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can ... 
Counting configurationfree sets in groups
(20170101)
Article
Open Access© 2017 Elsevier Ltd. We provide asymptotic counting for the number of subsets of given size which are free of certain configurations in finite groups. Applications include sets without solutions to equations in nonabelian ... 
On subsets of the normal rational curve
(20170601)
Article
Open AccessA normal rational curve of the (k1) dimensional projective space over Fq is an arc of size q+1 , since any k points of the curve span the whole space. In this paper, we will prove that if q is odd, then a subset of size ...