### 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 |
---|---|

Pages (from-to) | 331-342 |

Number of pages | 12 |

Journal | Australasian Journal of Combinatorics |

Volume | 34 |

Publication status | Published - 2006 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Australasian Journal of Combinatorics*,

*34*, 331-342.

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

Research output: Contribution to journal › Article

*Australasian Journal of Combinatorics*, vol. 34, pp. 331-342.

}

TY - JOUR

T1 - Weighted Ramsey problem

AU - Fujisawa, Jun

AU - Ota, Katsuhiro

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84885812037&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885812037&partnerID=8YFLogxK

M3 - Article

VL - 34

SP - 331

EP - 342

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

ER -