37 research outputs found
On the Factorization of Graphs with Exactly One Vertex of Infinite Degree
AbstractWe give a necessary and sufficient condition for the existence of a 1-factor in graphs with exactly one vertex of infinite degree
Grafos infinitos
Universidad de Sevilla. Grado en Matemática
Halmazelmélet; Partíció kalkulus, Végtelen gráfok elmélete = Set Theory; Partition Calculus , Theory of Infinite Graphs
Előzetes tervünknek megfelelően a halmazelmélet alábbi területein végeztünk kutatást és értünk el számos eredményt: I. Kombinatorika II. A valósak számsosságinvariánsai és ideálelmélet III. Halmazelméleti topológia Ezek mellett Sági Gábor kiterjedt kutatást végzett a modellelmélet területén , amely eredmények kapcsolódnak a kombinatorikához is. Eredményeinket 38 közleményben publikáltuk, amelyek majdnem mind az adott terület vezető nemzetközi lapjaiban jelentel meg (5 cikket csak benyújtottunk). Számos nemzetközi konferencián is résztvettünk, és hárman közűlünk (Juhász, Sádi, Soukup) plenáris/meghívott előadók voltak számos alkalommal. | Following our research plan, we have mainly done research -- and established a number of significant results -- in several areas of set theory: I. Combinatorics II. Cardinal invariants of the continuum and ideal theory III. Set-theoretic topology In addition to these, G. Sági has done extended research in model theory that had ramifications to combinatorics. We presented our results in 38 publications, almost all of which appeared or will appear in the leading international journals of these fields (5 of these papers have been submitted but not accepted as yet). We also participated at a number of international conferences, three of us (Juhász, Sági, Soukup) as plenary and/or invited speakers at many of these
La teoria de Ramsey infinita. Una mica d'història i alguns resultats recents.
L'origen de la combinatòria es troba en l'anomenat principi de les caselles de Dirichlet, també conegut com el principi Pigeonhole, segons el qual si en n caselles hi col. loquem més de n objectes, aleshores en alguna casella hi haurà almenys dos objectes. Per exemple, si repartim 6 coloms en 5 caselles, aleshores en alguna de les caselles hi haurà d'haver almenys 2 coloms..
On Minrank and Forbidden Subgraphs
The minrank over a field of a graph on the vertex set
is the minimum possible rank of a matrix such that for every , and
for every distinct non-adjacent vertices and in . For an
integer , a graph , and a field , let
denote the maximum possible minrank over of an -vertex graph
whose complement contains no copy of . In this paper we study this quantity
for various graphs and fields . For finite fields, we prove by
a probabilistic argument a general lower bound on , which
yields a nearly tight bound of for the triangle
. For the real field, we prove by an explicit construction that for
every non-bipartite graph , for some
. As a by-product of this construction, we disprove a
conjecture of Codenotti, Pudl\'ak, and Resta. The results are motivated by
questions in information theory, circuit complexity, and geometry.Comment: 15 page