We investigate paths, cycles and wheels in graphs with independence number of at most 2, in particular we prove theorems characterizing all such graphs which are hamiltonian. Ramsey numbers of the form R (G,K3), for G being a path, a cycle or a wheel, are known to be 2n (G) - 1, except for some small cases. In this paper we derive and count all critical graphs 1 for these Ramsey numbers.
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Australasian Journal of Combinatorics 9 (1994) 221-232
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