Ramsey numbers r(K3, G) for connected graphs G of order seven

AbstractThe triangle-graph Ramsey numbers are determined for all 814 of the 853 connected graphs of order seven. For the remaining 39 graphs lower and upper bounds are improved

The Ramsey number r(C₇,C₇,C₇)

Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support