Restricted size Ramsey number for 2K2 versus disconnected graphs of order six. Issue 1 (January 2021)

• Record Type: Journal Article
• Authors: Safitri, E; John, P; Silaban, D R
• Is Part Of: Journal of physics. Volume 1722:Issue 1(2021)
• Publication Date: 2021-01
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1722/1/012048
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: Given simple graphs F, G, and H . We say F arrows ( G, H ) if for any red-blue coloring of the edge of F, we find either a red-colored graph G or a blue-colored graph H . The Ramsey number r ( G, H ) is the smallest positive integer r such that a complete graph K r arrows ( G, H ). The size Ramsey number is the smallest positive integer r ˆ such that a graph F with the size of r ˆ arrows ( G, H ). The restricted size Ramsey number is the smallest positive integer r ∗ such that a graph F, of order r ( G, H ) with the size of r ∗, arrows ( G, H ). In this paper we give the restricted size Ramsey number of a matching of two edges and any disconnected graphs of order six with no isolates.