Abstract
Fouquet and Jolivet conjectured that a k-connected graph of order n and independence number α ≥ k has a cycle of length at least $$\frac {k(n+\alpha -k)}{\alpha}$$[Fouquet and Jolivet, Problemes combinatoires et theorie des graphes Orsay (1976), Problems, page 438]. Here we prove this conjecture for k=3.
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