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k ‐ordered Hamiltonian graphs
Author(s) -
Ng Lenhard,
Schultz Michelle
Publication year - 1997
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199701)24:1<45::aid-jgt6>3.0.co;2-j
Subject(s) - combinatorics , hamiltonian path , mathematics , hamiltonian (control theory) , hamiltonian path problem , graph , pancyclic graph , discrete mathematics , chordal graph , 1 planar graph , mathematical optimization
A hamiltonian graph G of order n is k ‐ordered, 2 ≤ k ≤ n , if for every sequence v 1 , v 2 , …, v k of k distinct vertices of G , there exists a hamiltonian cycle that encounters v 1 , v 2 , …, v k in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k ‐ordered hamiltonian graphs. The existence of k ‐ordered graphs with small maximum degree is investigated; in particular, a family of 4‐regular 4‐ordered graphs is described. A graph G of order n ≥ 3 is k ‐hamiltonian‐connected, 2 ≤ k ≤ n , if for every sequence v 1 , v 2 , …, v k of k distinct vertices, G contains a v 1 ‐ v k hamiltonian path that encounters v 1 , v 2 ,…, v k in this order. It is shown that for k ≥ 3, every ( k + 1)‐hamiltonian‐connected graph is k ‐ordered and a result of Ore on hamiltonian‐connected graphs is generalized to k ‐hamiltonian‐connected graphs. © 1997 John Wiley & Sons, Inc.