一些关于C4对星的Set Ramsey 数
Some Values of Set Ramsey Numbers forC4 versus Stars
DOI: 10.12677/AAM.2024.132082, PDF, 下载: 62  浏览: 112 
作者: 熊慧芸：浙江师范大学数学科学学院，浙江 金华
关键词: 有限射影平面；极性图；多部图；Set Ramsey数；Finite Projective Plane； Polarity Graph； Multipartite Diagram； Set Ramsey Number
摘要: 运用参数坐标构造出一个有限射影平面，由射影平面与射影平面上一个极性映射导出极性图. 根据 极性图, 对于一些 n，能够构造出 C4 对星 K1,n 的 set Ramsey 数 Ms(C4, K1,n) 的极值图。 由此 得到了关于这部分 n 的 Ms(C4, K1,n) 的下界并确定了一些新的精确值。
Abstract: A finite projective plane is constructed using parametric coordinates, and a polarity graph is derived from a polarity mapping and the projective plane. For some n, we can construct the extreme graph of set Ramsey numbers for C4 versus stars K1,n according to the polarity graph. The lower bound of Ms(C4, K1,n) is obtained and some new exact values are determined.
文章引用：熊慧芸. 一些关于C4对星的Set Ramsey 数[J]. 应用数学进展, 2024, 13(2): 869-876. https://doi.org/10.12677/AAM.2024.132082

参考文献

[1] Burger, A.P. and Vuuren, J.H.V. (2004) Ramsey Numbers in Complete Balanced Multipartite Graphs. Part I: Set Numbers. Discrete Mathematics, 283, 37-43.
https://doi.org/10.1016/j.disc.2004.02.004
[2] Magnant, C. and Yusko, A. (2011) Ramsey Set Numbers in Balanced Complete Multipartite Graphs. Journal of Combinatorial Mathematics and Combinatorial Computing, 77, 187.
[3] Goncalves, C.J.F., Carmelo, E.L.M. and Nakaoka, I.N. (2021) Polarity Graphs and C4-Free Multipartite Graphs. Procedia Computer Science, 195, 437-444.
https://doi.org/10.1016/j.procs.2021.11.053
[4] Parsons, T.D. (1976) Graphs from Projective Planes. Aequationes Mathematicae, 14, 167-189.
https://doi.org/10.1007/BF01836217

为你推荐