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- W2000561066 abstract "A graph G of order n is k-ordered hamiltonian, 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. In this paper, we generalize two well-known theorems of Chartrand on hamiltonicity of iterated line graphs to k-ordered hamiltonicity. We prove that if Ln(G) is k-ordered hamiltonian and n is sufficiently large, then Ln+1(G) is (k+1)-ordered hamiltonian. Furthermore, for any connected graph G, which is not a path, cycle, or the claw K1,3, there exists an integer N′ such that LN′+(k−3)(G) is k-ordered hamiltonian for k≥3." @default.
- W2000561066 created "2016-06-24" @default.
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- W2000561066 date "2009-04-01" @default.
- W2000561066 modified "2023-09-29" @default.
- W2000561066 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si7.gif display=inline overflow=scroll><mml:mi>k</mml:mi></mml:math>-ordered hamiltonicity of iterated line graphs" @default.
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- W2000561066 doi "https://doi.org/10.1016/j.disc.2008.02.044" @default.
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