摘要
Let G be a graph of order n with minimum degree δ(G)≥n/2+1. Faudree and Li(2012) conjectured that for any pair of vertices x and y in G and any integer 2≤k≤n/2, there exists a Hamiltonian cycle C such that the distance between x and y on C is k. In this paper, we prove that this conjecture is true for graphs of sufficiently large order. The main tools of our proof are the regularity lemma of Szemer′edi and the blow-up lemma of Koml′os et al.(1997).
Let G be a graph of order n with minimum degree δ（G）≥n/2＋1. Faudree and Li（2012） conjectured that for any pair of vertices x and y in G and any integer 2≤k≤n/2, there exists a Hamiltonian cycle C such that the distance between x and y on C is k. In this paper, we prove that this conjecture is true for graphs of sufficiently large order. The main tools of our proof are the regularity lemma of Szemer′edi and the blow-up lemma of Koml′os et al.（1997）.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11601093 and 11671296)
