# 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 language English 331-342 12 Australasian Journal of Combinatorics 34 Published - 2006

### Fingerprint

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

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

Research output: Contribution to journalArticle

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