Star-Critical connected ramsey numbers for 2-colorings of complete graphs

Moun, Monu; Jakhar, Jagjeet; Budden, Mark

doi:10.22108/toc.2024.140839.2157

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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. [2] M. Budden, Ramsey numbers for connected 2-colorings of complete graphs, Theory Appl. Graphs, 10 no. 1 (2023) Art. 7 10 pp. [3] M. Budden, Star-critical Ramsey numbers for graphs, SpringerBriefs in Mathematics, Springer, Cham, 2023. [4] M. Budden and T. Wimbish, Connected Ramsey numbers involving trees, under review. [5] L. Gerencsér and A. Gyárfás, On Ramsey-type problems, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 10 (1967) 167–170. [6] F. Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London, 1969. [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. [8] J. Hook, The classification of critical graphs and star-critical Ramsey numbers, dissertation, Lehigh University, 2010. [9] J. Hook and G. Isaak, Star-critical Ramsey numbers, Discrete Appl. Math., 159 no. 5 (2011) 328–334. [10] C. Magnant and P. Salehi Nowbandegani, Topics in Gallai-Ramsey theory, SpringerBriefs in Mathematics, Springer, Cham, 2020. [11] S. Radziszowski, Small Ramsey numbers- revision #17, Electron. J. Combin., DS1.17 (2024) 133 pp. [12] F. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2), 30 no. 4 (1929) 264–286. [13] D. Sumner, The connected Ramsey number, Discrete Math., 22 no. 1 (1978) 49–55.
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Star-Critical connected ramsey numbers for 2-colorings of complete graphs