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Bounds for the ramsey number of a disconnected graph versus any graph
Author(s) -
Gould Ronald J.,
Jacobson Michael S.
Publication year - 1982
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190060405
Subject(s) - ramsey's theorem , combinatorics , mathematics , graph , discrete mathematics , triangle free graph , domination analysis , graph power , line graph , vertex (graph theory)
Bounds are determined for the Ramsey number of the union of graphs versus a fixed graph H , based on the Ramsey number of the components versus H . For certain unions of graphs, the exact Ramsey number is determined. From these formulas, some new Ramsey numbers are indicated. In particular, if. Where k i is the number of components of order i and t 1 ( H ) is the minimum order of a color class over all critical colorings of the vertices of H , then.