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Star-critical connected Ramsey numbers for 2-colorings of complete graphs | ||
Transactions on Combinatorics | ||
مقاله 2، دوره 14، شماره 4، اسفند 2025، صفحه 211-222 اصل مقاله (448.39 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 | ||
سایر فایل های مرتبط با مقاله
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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. [7] F. Harary, Recent results on generalized Ramsey theory for graphs, Graph theory and applications (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1972), Lecture Notes in Math., 303, Springer, Berlin New York, 1972 125–138. [11] S. Radziszowski, Small Ramsey numbers- revision #17, Electron. J. Combin., DS1.17 (2024) 133 pp. | ||
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