Abstract
A graph G is quasi-claw-free if it satisfies the property: d(x,y)=2 ⇒ there exists 
such that 
. In the paper, we prove that the circumference of a 3-connected quasi-claw-free graph G on n vertices is at least min{4δ−2,n} and G is hamiltonian if n≤5δ−5.
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Vumar, E. On the Circumference of 3-Connected Quasi-Claw-Free Graphs. Graphs and Combinatorics 22, 271–282 (2006). https://doi.org/10.1007/s00373-006-0650-7
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DOI: https://doi.org/10.1007/s00373-006-0650-7