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Discrete Mathematics. 01/2008; 308:5325-5333.
Electronic Notes in Discrete Mathematics. 01/2005; 22:93-99.
ABSTRACT: We show that if G is a 4-connected claw-free graph in which every induced hourglass subgraph S contains two non-adjacent vertices with a common neighbor outside S, then G is hamiltonian. This extends the fact that 4-connected claw-free, hourglass-free graphs are hamiltonian, thus proving a broader special case of a conjecture by Matthews and Sumner.