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Article Dans Une Revue Science China Mathematics Année : 2018

Distributing pairs of vertices on Hamiltonian cycles

Hao Li
Qiang Sun

Résumé

AbstractLet G be a graph of order n with minimum degree δ(G)⩾n2+1δ(G)⩾n2+1\delta (G) \geqslant \tfrac{n} {2} + 1δ(G)⩾n2+1. Faudree and Li (2012) conjectured that for any pair of vertices x and y in G and any integer 2⩽k⩽n22⩽k⩽n22 \leqslant k \leqslant \tfrac{n} {2}2⩽k⩽n2, 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 Szemerédi and the Blow-up lemma of Komlós et al. (1997).
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Dates et versions

hal-01763169 , version 1 (10-04-2018)

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Hao Li, Weihua He, Qiang Sun. Distributing pairs of vertices on Hamiltonian cycles. Science China Mathematics, In press, 5, pp.955-972. ⟨10.1007/s11425-016-9057-x⟩. ⟨hal-01763169⟩
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