کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
420345 | 683925 | 2010 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Degree conditions on distance 2 vertices that imply kk-ordered Hamiltonian Degree conditions on distance 2 vertices that imply kk-ordered Hamiltonian](/preview/png/420345.png)
For a positive integer kk, a graph GG is kk-ordered if for every ordered set of kk vertices, there is a cycle that encounters the vertices of the set in the given order. If the cycle is also a Hamiltonian cycle, then GG is said to be kk-ordered Hamiltonian. We first show that if GG is a (k+1)(k+1)-connected, kk-ordered graph of order n≥4k+3n≥4k+3 and d(u)+d(v)≥n−1d(u)+d(v)≥n−1 for every pair of vertices uu and vv of GG with d(u,v)=2d(u,v)=2, then GG is kk-ordered Hamiltonian unless GG belongs to an exceptional class of graphs. The latter class is described in this paper. By this result, we prove that GG is kk-ordered Hamiltonian if GG has the order n≥27k3n≥27k3 and d(u)+d(v)≥n+(3k−9)/2d(u)+d(v)≥n+(3k−9)/2 for every pair of vertices uu and vv of GG with d(u,v)=2d(u,v)=2.
Journal: Discrete Applied Mathematics - Volume 158, Issue 4, 28 February 2010, Pages 331–339