Barycentric sequences and barycentric Ramsey numbers stars

Delorme, Charles; González, Samuel Jaramillo; Ordaz, Oscar; Varela, María Teresa

doi:10.1016/s0012-365x(03)00153-5

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Note that the motivation of Definition 4 is the following definition of -barycentric sequence which was introduced in [9] and has already been used in graph labeling problems, specially in Ramsey theory [9][10][11]. Example 6.…”

Section: Lemma 1 a Graph Ismentioning

confidence: 99%

On the Barycentric Labeling of Certain Graphs

Alikhani

Amirzadeh

2014

Journal of Discrete Mathematics

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Let be an abelian group. A graph is called -magic if there exists edge labeling : ( ) → \ {0} such that the induced vertex set labeling, where the sum is over all edges in ( ), is a constant map.A graph is -barycentric-magic (or has -barycentric labeling) if is -magic and also satisfiesfor all V ∈ and for some vertex V adjacent to V. In this paper we consider some graphs and characterize all ∈ N for which is Z -barycentric-magic.

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Section: Lemma 1 a Graph Ismentioning

confidence: 99%

On the Barycentric Labeling of Certain Graphs

Alikhani

Amirzadeh

2014

Journal of Discrete Mathematics

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“…El estudio de las secuencias k-baricéntricas se inician en [5] y [6]. En [6] la constante de Davenport Baricéntrica, BD(G), es decir, el menor entero positivo t tal que toda t-secuencia en G contiene una subsecuencia baricéntrica.…”

Section: Introductionunclassified

“…En [6] la constante de Davenport Baricéntrica, BD(G), es decir, el menor entero positivo t tal que toda t-secuencia en G contiene una subsecuencia baricéntrica. En [5] la constante de Davenport k-baricéntrica, BD(k, G), se define como el menor entero positivo t tal que toda t-secuencia en G contiene una subsecuencia k-baricéntrica.…”

Section: Introductionunclassified

Un método algoritmo para el cálculo del número baricéntrico de Ramsey para el grafo estrella

Villarroel¹,

Figueroa

Márquez³

et al. 2018

bspm

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Let G be an abelian finite group and H be a graph. A sequence in G, with length al least two, is barycentric if it contains an "average" element of its terms. Within the context of these sequences, one defines the barycentric Ramsey number, denoted by BR(H, G), as the smallest positive integer t such that any coloration of the edges of the complete graph Kt with elements of G produces a barycentric copy of the graph H. In this work we present a method based on the combinatorial theory and on the definition of barycentric Ramsey for calculating exact values of the above metioned constant, for some small graphs where the order is less than or equal to 8. We will exemplify the case where H is the star graph K 1,k , and where G is the cyclical group Zn, with 3 ≤ n ≤ 11 and 3 ≤ k ≤ n.

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“…Motivated among others by results of Y. Ould Hamidoune, such as [9], systematic investigations related to the following 'pattern' have been started in [4,5] and continued for instance in [13,16]; for a survey see [15]. A very closely related problem also appears in some work of Alon [1], and special cases are classical (cf.…”

Section: Introductionmentioning

confidence: 99%