Type: Article
Publication Date: 1983-03-01
Citations: 74
DOI: https://doi.org/10.1002/jgt.3190070106
Abstract Chvátal has shown that if T is a tree on n points then r ( K k , T ) = ( k – 1) ( n – 1) + 1, where r is the (generalized) Ramsey number. It is shown that the same result holds when T is replaced by many other graphs. Such a T is called k ‐good. The results proved all support the conjecture that any large graph that is sufficiently sparse, in the appropriate sense, is k ‐good.