## Abstract

Let F, G, and H be simple graphs. We say F → (G, H) if for every 2-coloring of the edges of F there exist a monochromatic G or H in F. The Ramsey number r(G, H) is defined as min {|V (F)|: F → (G, H)}, the size Ramsey number r(G, H) is defined as min {|E(F)|: F → (G, H)}, and the restricted size Ramsey number r∗(G, H) is defined as min {|E(F)|: F → (G, H), |V (F)| = r(G, H)}. In this paper we give a lower bound for the restricted size Ramsey number for a path P_{3} versus P_{n}. We also give the upper bound and the exact restricted size Ramsey number for some small values of n.

Original language | English |
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Title of host publication | Proceedings of the 7th SEAMS UGM International Conference on Mathematics and Its Applications 2015 |

Subtitle of host publication | Enhancing the Role of Mathematics in Interdisciplinary Research |

Editors | Yeni Susanti, Indah Emilia Wijayanti, Fajar Adi Kusumo, Irwan Endrayanto Aluicius |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735413542 |

DOIs | |

Publication status | Published - 11 Feb 2016 |

Event | 7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research - Yogyakarta, Indonesia Duration: 18 Aug 2015 → 21 Aug 2015 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1707 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 7th SEAMS UGM International Conference on Mathematics and Its Applications: Enhancing the Role of Mathematics in Interdisciplinary Research |
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Country/Territory | Indonesia |

City | Yogyakarta |

Period | 18/08/15 → 21/08/15 |

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