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Graphs and Combinatorics

, Volume 36, Issue 1, pp 167–176 | Cite as

Long Paths in Bipartite Graphs and Path-Bistar Bipartite Ramsey Numbers

  • Michitaka FuruyaEmail author
  • Shun-ichi Maezawa
  • Kenta Ozeki
Original Paper
  • 31 Downloads

Abstract

In this paper, we focus on a so-called Fan-type condition assuring us the existence of long paths in bipartite graphs. As a consequence of our main result, we completely determine the bipartite Ramsey numbers \(b(P_{s},B_{t_{1},t_{2}})\), where \(B_{t_{1},t_{2}}\) is the graph obtained from a \(t_{1}\)-star and a \(t_{2}\)-star by joining their centers.

Keywords

Fan-type condition Bipartite Ramsey number Bistar Bipartite graph 

Mathematics Subject Classification

05C55 05C38 05C07 

Notes

Acknowledgements

This work was supported by JSPS KAKENHI Grant number 18K13449 (to M.F).

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Liberal Arts and SciencesKitasato UniversitySagamiharaJapan
  2. 2.Graduate School of Environment and Information SciencesYokohama National UniversityYokohamaJapan
  3. 3.Faculty of Environment and Information SciencesYokohama National UniversityYokohamaJapan

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