Star-critical connected Ramsey numbers for 2-colorings of complete graphs
نویسندگان
1 Department of Mathematics, Central University of Haryana, Haryana, India.
2 Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723
3 Department of Mathematics, Central University of Haryana, Haryana, India
doi
10.22108/toc.2024.140839.2157چکیده
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.
