Weighted Ramsey problem

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A weighted graph is one in which every edge e is assigned a nonnegative number, called the weight of e. The weight of a graph is defined as the sum of the weights of its edges. In 2-edge-c.olored complete graph, by using Ramsey-type theorems, we obtain the existence of monochromatic subgraph which have many edges compared with its order. In this paper, we extend the concept of Ramsey problem to the weighted graphs, and we show the existence of a heavy monochromatic subgraph in 2-edge-colored graph with small order.

Original languageEnglish
Pages (from-to)331-342
Number of pages12
JournalAustralasian Journal of Combinatorics
Volume34
Publication statusPublished - 2006

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Weighted Graph
Subgraph
Edge-colored Graph
Complete Graph
Non-negative
Graph in graph theory
Theorem
Concepts

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Weighted Ramsey problem. / Fujisawa, Jun; Ota, Katsuhiro.

In: Australasian Journal of Combinatorics, Vol. 34, 2006, p. 331-342.

Research output: Contribution to journalArticle

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