|
|
三色二部拉姆齐数 Rb(C4, C4, Pn)
|
Abstract:
本文研究了与四圈和路有关的二部拉姆齐数，给出了 n 较小时二部拉姆齐数 Rb(C4, C4, Pn) 的值，并给出了一般上界。
This paper studies bipartite Ramsey numbers related to cycles of length four and paths, and gives the values of the bipartite Ramsey number Rb(C4, C4, Pn) for small n and provides a general upper bound.
| [1] | Ramsey, F.P. (2009) On a Problem of Formal Logic. In: Gessel, I. and Rota, G.C., Eds., Classic Papers in Combinatorics, Birkh？user Boston, 1-24. https://doi.org/10.1007/978-0-8176-4842-8_1 |
| [2] | Sun, Y., Yang, Y., Lin, X. and Zheng, W. (2007) On the Three-Color Ramsey Numbers R(C4, C4, Cn). Ars Combinatoria, 84, 3-11. |
| [3] | 刘敏. 关于 4-圈的 3-色 Ramsey 数 [D]: [硕士学位论文]. 金华: 浙江师范大学, 2020. |
| [4] | Wang, K., Zhou, J., He, D. and Tong, Q. (2021) Note on the Three-Coloured Bipartite Ram- sey Numbers for Paths. International Journal of Computer Mathematics: Computer Systems Theory, 6, 189-193. https://doi.org/10.1080/23799927.2021.1934900 |
| [5] | Lakshmi, R. and Sindhu, D.G. (2020) Three-Colour Bipartite Ramsey Number Rb(G1, G2, P3). Electronic Journal of Graph Theory and Applications, 8, 195-204. https://doi.org/10.5614/ejgta.2020.8.1.14 |
| [6] | Zarankiewicz, K. (1951) Problem P 101. Colloquium Mathematicum, 2, 5. |
| [7] | Guy, R.K. (1969) A Many-Facetted Problem of Zarankiewicz. In: Chartrand, G. and Kapoor, S.F., Eds., The Many Facets of Graph Theory. Lecture Notes in Mathematics, Springer Berlin Heidelberg, 129-148. https://doi.org/10.1007/bfb0060112 |
| [8] | Gyárfás, A., Rousseau, C.C. and Schelp, R.H. (1984) An Extremal Problem for Paths in Bipartite Graphs. Journal of Graph Theory, 8, 83-95. https://doi.org/10.1002/jgt.3190080109 |
| [9] | Rowshan, Y. and Gholami, M. (2022) Multicolor Bipartite Ramsey Numbers for Paths, Cycles, and Stripes. Computational and Applied Mathematics, 42, Article No. 25. https://doi.org/10.1007/s40314-022-02166-w |
