论文信息 - Quadrangularly connected claw-free graphs

Quadrangularly connected claw-free graphs

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 ([email protected][email protected]?4)C"1,C"2,...,C"r such that e"[email protected]?E(C"1) and e"[email protected]?E(C"r) and E(C"i)@?E(C"i"+"1) @A 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. [email protected]?ek [Hamiltonian circuits in N"2-locally connected K"1","3-free graphs, J. Graph Theory 14 (1990) 321-331] and other known results.

Hong-Jian Lai | Mingchu Li | Cheng Guo | Liming Xiong | Dengxin Li

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