The IRMA Community
Newsletters
Research IRM
Click a keyword to search titles using our InfoSci-OnDemand powered search:
|
Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices
Abstract
A popular area of graph theory is based on a paper written in 1930 by F. P. Ramsey titled “On a Problem on Formal Logic.” A theorem which was proved in his paper triggered the study of modern Ramsey theory. However, his premature death at the young age of 26 hindered the development of this area of study at the initial stages. The balanced size multipartite Ramsey number mj (H,G) is defined as the smallest positive number s such that Kj×s→ (H,G). There are 36 pairs of (H, G), when H, G represent connected graphs on four vertices (as there are only 6 non-isomorphic connected graphs on four vertices). In this chapter, the authors find mj (H, G) exhaustively for all such pairs in the tripartite case j=3, and in the quadpartite case j=4, excluding the case m4 (K4,K4). In this case, the only known result is that m4 (K4,K4) is greater than or equal to 4, since no upper bound has been found as yet.
Related Content
Vinod Kumar, Himanshu Prajapati, Sasikala Ponnusamy.
© 2023.
18 pages.
|
Sougatamoy Biswas.
© 2023.
14 pages.
|
Ganga Devi S. V. S..
© 2023.
10 pages.
|
Gotam Singh Lalotra, Ashok Sharma, Barun Kumar Bhatti, Suresh Singh.
© 2023.
15 pages.
|
Nimish Kumar, Himanshu Verma, Yogesh Kumar Sharma.
© 2023.
16 pages.
|
R. Soujanya, Ravi Mohan Sharma, Manish Manish Maheshwari, Divya Prakash Shrivastava.
© 2023.
12 pages.
|
Nimish Kumar, Himanshu Verma, Yogesh Kumar Sharma.
© 2023.
22 pages.
|
|
|