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Distributing pairs of vertices on Hamiltonian cycles
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作者 Weihua He Hao Li Qiang Sun 《Science China Mathematics》 SCIE CSCD 2018年第5期955-972,共18页
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 dis... 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). 展开更多
关键词 Hamiltonian cycle faudree-li conjecture regularity lemma blow-up lemma
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