BOZA PRIETO , Luis

Los primeros problemas que plantearon y resolvieron en Teoría de Grafos, son problemas referentes a la Transversalidad de Grafos (la posibilidad de recorrer o bien las aristas o bien los vértices de un grafo sin repetición), así el Problema de los Puentes de Konigsbe rg, con el que nace la disciplina, resuelto por L. Euler en 1736 [10] o el...

For two given graphs G1 and G2, the Ramsey number r(G1,G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the comple ment of G contains G2. Let Km denote a complete graph of order m and Kn − P3 a complete graph of order n without two incident edges. In this paper, we prove that r(K5 − P3,K5) = 25 without...

For each graph G the dimension of G is defined as the smallest dimension in the Euclidean Space where there is an embedding in which all the edges of G are segments of a straight line of length one. The exact value is calculated for some important families of graphs and this value is compared with other invariants. An infinite quantity of...

En este traba jo se procede a recapitular resultados conocidos sobre el problema de caracterizar los grafos que admiten inmersiones en super cies y en seudosuper - cies con todos los v ertices en la misma cara y se da una caracterizaci on original de los grafos con dicha propiedad en seudosuper cies que surgen de manera natural y que han sido...

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For given graphs H1, H2, H3, the 3-color Ramsey number R(H1, H2, H3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it always contains a monochromatic copy of Hi colored with i, for some 1 6 i 6 3. We study the bounds on 3-color Ramsey numbers R(H1, H2, H3), where...

We define a new association between graphs and orthonormal bases of even-dimensional Euclidean vector spaces endowed with an spe cial isomorphism motivated by the recently introduced theory of submanifolds associated with graphs. We provide several interest ing examples and we analyze the shape of such graphs by proving some general results.

In this paper, we describe a new method to classify complex filiform Lie algebras based on the concept of isomorphism between Lie algebras. This method, which has the advantage of being applied to any dimension, gives the families of algebras in each dimension in an explicit way. In order to apply, only the corresponding structure the- orem of...

Chartrand and Harary characterized finite outer-planar graphs, and Wagner studied uncountable graphs admitting a planar embedding. We continue this research for those outer-S graphs in surfaces S by studying un countable graphs admitting S-embeddings with all their vertices in the same face (namely, outer-S embeddings).

In this paper we give the explicit classification of complex filiform Lie algebras of dimension 11. To do this, we use a method previously obtained by us in an earlier paper, which is based on the concept of isomorphism between Lie algebras. At present, this explicit classification is not known, although Gomez, Jim enez and Khakimdjanov...

In this paper we explicitly characterize the outer-embeddings without vertex accumulation points in the open cylinder and in the Mo¨bius strip. In the first case, the list of forbidden minors consists of 11 graphs. In the second, we provide the list of 92 forbidden minors as well as the list of 182 forbidden subgraphs.

In this paper we study graph embeddings in pseudosurfaces formed by three spheres sharing at most two points each pair, and in such a way that all vertices in the graph are in the same face. Our results and examples show that the behaviour of outer embeddings in these pseudosurfaces is rather different from embeddings on the...

In this expository paper we revise some extensions of Kuratowski planarity criterion, providing a link between the embeddings of infinite graphs without accumulation points and the embeddings of finite graphs with some distinguished vertices in only one face. This link is valid for any surface and for some pseudosurfaces. On the one hand, we...

In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs

In this note we extend the notion of the center of a graph to infinite graphs. Thus, a vertex is in the center of the infinite graph G if it is in the center of an increasing family of finite subgraphs covering G. We give different characterizations of when a vertex is in the center of an infinite graph and we prove that any infinite graph with...

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For integers k, n with k, n ≥ 1, the n-color weak Schur number W Sk(n) is defined as the least integer N, such that for every n-coloring of the integer interval [1, N], there exists a monochromatic solution x1, . . . , xk, xk+1 in that interval to the equation x1 +x2 +. . .+xk = xk+1, with xi 6= xj , when i 6= j. We show a relationship...

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In this study, we focus on the concept of the 2-color off-diagonal generalized weak Schur numbers, denoted as WS(2; k1, k2). These numbers are defined for integers ki ≥ 2, where i = 1, 2, as the smallest integer M, such that any 2-coloring of the integer interval [1, M] must contain a 2-colored solution to the equation Ekj: x1 + x2 + ... + xkj...