For integers k, n with k, n ≥ 1, the n-color weak Schur number WSk (n) is defined as the least integer N, such that for ...

In this study, we focus on the concept of the 2-color off-diagonal generalized weak Schur numbers, denoted as WS(2; k1, ...

Let k ≥ 3 be an integer, the Schur number Sk(3) is the least positive integer, such that for every 3-coloring of the integer ...

For integers k, n, c with k, n ≥ 1, and c ≥ 0, the n-color weak Rado number WRk (n, c) is defined as the least integer N, ...

Given any length k ≥ 3 and density 0 < δ ≤ 1, we introduce and study the set Sz(k, δ) consisting of all positive integers ...

Given k ≥ 1, the Fox–Kleitman conjecture from 2006 states that there exists a nonzero integer b such that the 2k-variable ...

We show that, for every positive integer r, there exists an integer b = b(r) such that the 4-variable quadratic Diophantine equation (x1 − y1)(x2 − y2) = b is r-regular. Our proof uses Szemerédi’s theorem on arithmetic progressions.

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 ...

For integers k, n, c with k, n ≥ 1, the n-color Rado number Rk(n, c) is defined to be the least integer N if any, or ...

For integers k, n, c with k, n ≥ 1 and c ≥ 0, the n color weak Rado number W Rk(n, c) is defined as the least integer N, ...

For integers k, n, c with k, n ≥ 1, the n-color Rado number Rk(n, c) is defined to be the least integer N, if it exists ...

The main goal of this paper is to show an application of Graph Theory to classifying Lie algebras over finite fields. It ...

The problem of Lie algebras’ classification, in their different varieties, has been dealt with by theory researchers since ...

In this expository paper we revise some extensions of Kuratowski planarity criterion, providing a link between the embeddings ...

For graphs G1, . . . , Gs, the multicolor Ramsey number R(G1, . . . , Gs) is the smallest integer r such that if we give ...

For each graph G the dimension of G is defined as the smallest dimension in the Euclidean Space where there is an embedding ...

La memoria se enmarca en la "Teoría de Inmersiones de Grafos en Superficies", presentando y resolviendo varios e interesantes ...

Chartrand et al. (J. Combin. Theory Ser. B 10 (1971) 12–41) proved that the line graph of a graph G is outerplanar if and ...

El matemático alemán Euler (1707-1782) resolvió en 1736 el famoso problema de los puentes de Königsberg. Dicha ciudad ...

En este traba jo se procede a recapitular resultados conocidos sobre el problema de caracterizar los grafos que admiten ...

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 ...

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

Los primeros problemas que plantearon y resolvieron en Teoría de Grafos, son problemas referentes a la Transversalidad de ...