Open AccessRestricted size Ramsey number for 2K 2 versus disconnected graphs of order six
Author(s) -
Elfira Safitri,
Peter E. John,
Denny Riama Silaban
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1722/1/012048
Subject(s) - ramsey's theorem , combinatorics , graph , mathematics , algorithm
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.