Bounds for the ramsey number of a disconnected graph versus any graph | Zendy

Gould Ronald J. | Zendy; Jacobson Michael S. | Zendy

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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.

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