TY - JOUR

T1 - On k-ordered Hamiltonian graphs

AU - Kierstead, Henry

AU - Sárközy, G. N.

AU - Selkow, S. M.

PY - 1999/9

Y1 - 1999/9

N2 - A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Define f (k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine f (k, n) if n is sufficiently large in terms of k. Let g (k, n) = [n/2] + [k/2] - 1. More precisely, we show that f(k, n) = g(k, n) if n ≥ 11k - 3. Furthermore, we show that f(k,n) ≥ g(k, n) for any n ≥ 2k. Finally we show that f(k, n) > g(k, n) if 2k < n < 3k - 6.

AB - A Hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a Hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Define f (k, n) as the smallest integer m for which any graph on n vertices with minimum degree at least m is a k-ordered Hamiltonian graph. In this article, answering a question of Ng and Schultz, we determine f (k, n) if n is sufficiently large in terms of k. Let g (k, n) = [n/2] + [k/2] - 1. More precisely, we show that f(k, n) = g(k, n) if n ≥ 11k - 3. Furthermore, we show that f(k,n) ≥ g(k, n) for any n ≥ 2k. Finally we show that f(k, n) > g(k, n) if 2k < n < 3k - 6.

KW - Hamiltonian graph

KW - k-ordered

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U2 - 10.1002/(sici)1097-0118(199909)32:1<17::aid-jgt2>3.0.co;2-g

DO - 10.1002/(sici)1097-0118(199909)32:1<17::aid-jgt2>3.0.co;2-g

M3 - Article

AN - SCOPUS:0039008403

SN - 0364-9024

VL - 32

SP - 17

EP - 25

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 1

ER -