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, Problèmes combinatoires et théorie des graphes Orsay (1976), Problems, page 438]. Here we prove this conjecture for k=3.
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References
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Manoussakis, Y. Longest Cycles in 3-connected Graphs with Given Independence Number. Graphs and Combinatorics 25, 377–384 (2009). https://doi.org/10.1007/s00373-009-0846-8
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DOI: https://doi.org/10.1007/s00373-009-0846-8