Note on Locating Pairs of Vertices on Hamiltonian Cycles

Note on Locating Pairs of Vertices on Hamiltonian Cycles

Given a fixed positive integer k ≥ 2, let G be a simple graph of order n  ≥ 6 k . It is proved that if the minimum degree of G is at least n /2 + 1, then for every pair of vertices x and y , there exists a Hamiltonian cycle such that the distance between x and y along that cycle is precisely k ....

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Veröffentlicht in:Graphs and combinatorics 2014-07, Vol.30 (4), p.887-894
Hauptverfasser: Faudree, Ralph J., Lehel, Jeno, Yoshimoto, Kiyoshi
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Combinatorics
Engineering Design
Graphs
Integers
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung:Given a fixed positive integer k ≥ 2, let G be a simple graph of order n  ≥ 6 k . It is proved that if the minimum degree of G is at least n /2 + 1, then for every pair of vertices x and y , there exists a Hamiltonian cycle such that the distance between x and y along that cycle is precisely k .
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-013-1325-9