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All 2-Connected Claw-Free Graphs with Diameter at Most TWO are Hamiltonian
Author(s): 
Pages: 19-24
Year: Issue:  4
Journal: Operations Research Transactions

Keyword:  Operations researchline graphsclaw-free graphsclosed trailHamilton cycle;
Abstract: A graph iS called 2K2-free if it does not contain an independent pair of edges as an induced subgraph.Kriesell proved that all 4-connected line graphs of claw.free graph axe Hamiltonian-connected.Motivated from this,in this note,we show that if G is 2K2-free and is not isomorphic to K2,P3 or a double star,then the line graph L(G)isHamiltonian.Moreover,by applying the closure concept of claw-free graphs introduced byby Ainouche et al.,which says that every 2-connected claw-free graph of diameter at most 2 is Hamiltonian.
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