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- W2079821081 abstract "A graph G is quadrangularly connected if for every pair of edges e 1 and e 2 in E ( G ) , G has a sequence of l -cycles ( 3 ≤ l ≤ 4 ) C 1 , C 2 , … , C r such that e 1 ∈ E ( C 1 ) and e 2 ∈ E ( C r ) and E ( C i ) ∩ E ( C i + 1 ) ≠ ∅ for i = 1 , 2 , … , r - 1 . In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to either G 1 or G 2 such that N 1 ( x , G ) of every vertex x of degree 4 in H is disconnected is hamiltonian, which implies a result by Z. Ryjác˘ek [Hamiltonian circuits in N 2 -locally connected K 1 , 3 -free graphs, J. Graph Theory 14 (1990) 321–331] and other known results." @default.
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- W2079821081 date "2007-05-01" @default.
- W2079821081 modified "2023-09-28" @default.
- W2079821081 title "Quadrangularly connected claw-free graphs" @default.
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- W2079821081 doi "https://doi.org/10.1016/j.disc.2006.07.034" @default.
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