کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4649916 | 1342469 | 2008 | 8 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Degree conditions on claws and modified claws for hamiltonicity of graphs Degree conditions on claws and modified claws for hamiltonicity of graphs](/preview/png/4649916.png)
Ore presented a degree condition involving every pair of nonadjacent vertices for a graph to be hamiltonian. Fan [New sufficient conditions for cycles in graphs, J. Combin. Theory Ser. B 37 (1984) 221–227] showed that not all the pairs of nonadjacent vertices are required, but only the pairs of vertices at the distance two suffice. Bedrossian et al. [A generalization of Fan's condition for hamiltonicity, pancyclicity, and hamiltonian connectedness, Discrete Math. 115 (1993) 39–50] improved Fan's result involving the pairs of vertices contained in an induced claw or an induced modified claw. On the other hand, Matthews and Sumner [Longest paths and cycles in K1,3K1,3-free graphs, J. Graph Theory 9 (1985) 269–277] gave a minimum degree condition for a claw-free graph to be hamiltonian. In this paper, we give a new degree condition in an induced claw or an induced modified claw ensuring the hamiltonicity of graphs which extends both results of Bederossian et al. and Matthews and Sumner.
Journal: Discrete Mathematics - Volume 308, Issue 9, 6 May 2008, Pages 1612–1619