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Star-Critical connected ramsey numbers for 2-colorings of complete graphs | ||
Transactions on Combinatorics | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 مرداد 1403 اصل مقاله (448.61 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2024.140839.2157 | ||
نویسندگان | ||
Monu Moun1؛ Jagjeet Jakhar2؛ Mark Budden* 3 | ||
1Department of Mathematics, Central University of Haryana, Haryana, India | ||
2Department of Mathematics, Central University of Haryana, Haryana, India. | ||
3Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723 | ||
چکیده | ||
This paper builds upon Sumner's work by further investigating the concept of connected Ramsey numbers, specifically focusing on star-critical connected Ramsey numbers. We obtain star-critical connected Ramsey numbers for several cases of trees versus complete graphs, stars versus stars, and paths versus paths. The connected Ramsey number for a star versus $K_3$ is also evaluated. Exact values are also obtained for the connected Ramsey numbers of $K_{1,n}$ versus $K_3$. This research explores the interplay between connectivity and graph coloring within the context of Ramsey theory. | ||
کلیدواژهها | ||
Ramsey number؛ connected Ramsey number؛ star-critical Ramsey number | ||
مراجع | ||
[1] J. Bosák, A. Rosa and Š. Znám, On decompositions of complete graphs into factors with given diameters, Proc. Colloq., Tihany, 1966, Academic Press, New York-London, 1968 37–56. [11] S. Radziszowski, Small Ramsey numbers- revision #17, Electron. J. Combin., DS1.17 (2024) 133 pp. | ||
آمار تعداد مشاهده مقاله: 107 تعداد دریافت فایل اصل مقاله: 49 |