Mohd Latip, Fatin Nur Nadia Binti and Tan, Ta Sheng
(2021)
*A note on on-line Ramsey numbers of stars and paths.*
Bulletin of the Malaysian Mathematical Sciences Society, 44 (5).
pp. 3511-3521.
ISSN 0126-6705,
DOI https://doi.org/10.1007/s40840-021-01130-x.

## Abstract

An on-line Ramsey game is a game between two players, Builder and Painter, on an initially empty graph with unbounded set of vertices. In each round, Builder selects two vertices and joins them with an edge while Painter colours the edge immediately with either red or blue. Builder's aim is to force either a red copy of a fixed graph G or a blue copy of a fixed graph H. The game ends with Builder's victory when Builder manages to force either a red G or a blue H. The minimum number of rounds for Builder to win the game, regardless of Painter's strategy, is the on-line Ramsey number r (G, H). This note focuses on the case when G and H are stars and paths. In particular, we will prove the upper bound of r (S-3, Pl+1) <= 5l/3 + 2. We will also present an alternative proof for the upper bound of r (S-2 = P-3, Pl+1) = 5l/4].

Item Type: | Article |
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Funders: | Faculty of Science-University of Malaya Research Grant (RF017B-2018) |

Uncontrolled Keywords: | Ramsey theory; On-line Ramsey game; Stars; Paths |

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Institute of Mathematical Sciences |

Depositing User: | Ms Zaharah Ramly |

Date Deposited: | 09 Jun 2022 04:31 |

Last Modified: | 09 Jun 2022 04:31 |

URI: | http://eprints.um.edu.my/id/eprint/27558 |

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