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

Neighborhood conditions for graphs with induced claws

AbstractK1,4-free graphs with independent claw centers and a certain neighborhood property concerning the endvertices of the induced claws are proved to be pancyclic or Hamiltonian, depending on which of three different properties concerning induced modified claws they meet

Ramsey numbers r(K3, G) for G ≅ K7 − 2P2 and G ≅ K7 − 3P2

AbstractFor the graphs K7 − 2P2 and K7 − 3P2 we give a proof of their triangle-graph Ramsey numbers without using any computer support

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