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## Discussiones Mathematicae Graph Theory

2004 | 24 | 3 | 359-372
Tytuł artykułu

### Linear forests and ordered cycles

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A collection $L = P¹ ∪ P² ∪ ... ∪ P^t$ (1 ≤ t ≤ k) of t disjoint paths, s of them being singletons with |V(L)| = k is called a (k,t,s)-linear forest. A graph G is (k,t,s)-ordered if for every (k,t,s)-linear forest L in G there exists a cycle C in G that contains the paths of L in the designated order as subpaths. If the cycle is also a hamiltonian cycle, then G is said to be (k,t,s)-ordered hamiltonian. We give sharp sum of degree conditions for nonadjacent vertices that imply a graph is (k,t,s)-ordered hamiltonian.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
359-372
Opis fizyczny
Daty
wydano
2004
otrzymano
2002-08-02
poprawiono
2004-07-19
Twórcy
autor
• Georgia State University, Atlanta, GA 30303
autor
• University of Memphis, Memphis, TN 38152
autor
• Emory University, Atlanta, GA 30322
autor
• Emory University, Atlanta, GA 30322
autor
• Drew University, Madison, NJ 07940
autor
• Emory University, Atlanta, GA 30322, Technische Universität Berlin, Berlin, Germany
Bibliografia
• [1] B. Bollobás and A. Thomason, Highly Linked Graphs, Combinatorics, Probability, and Computing, (1993) 1-7.
• [2] J.R. Faudree, R.J. Faudree, R.J. Gould, M.S. Jacobson and L. Lesniak, On k-Ordered Graphs, J. Graph Theory 35 (2000) 69-82, doi: 10.1002/1097-0118(200010)35:2<69::AID-JGT1>3.0.CO;2-I
• [3] R.J. Faudree, R.J., Gould, A. Kostochka, L. Lesniak, I. Schiermeyer and A. Saito, Degree Conditions for k-ordered hamiltonian graphs, J. Graph Theory 42 (2003) 199-210, doi: 10.1002/jgt.10084.
• [4] Z. Hu, F. Tian and B. Wei, Long cycles through a linear forest, J. Combin. Theory (B) 82 (2001) 67-80, doi: 10.1006/jctb.2000.2022.
• [5] H. Kierstead, G. Sarkozy and S. Selkow, On k-Ordered Hamiltonian Graphs, J. Graph Theory 32 (1999) 17-25, doi: 10.1002/(SICI)1097-0118(199909)32:1<17::AID-JGT2>3.0.CO;2-G
• [6] W. Mader, Existenz von n-fach zusammenhängenden Teilgraphen in Graphen genügend grosser Kantendichte, Abh. Math. Sem. Univ. Hamburg 37 (1972) 86-97, doi: 10.1007/BF02993903.
• [7] L. Ng and M. Schultz, k-Ordered Hamiltonian Graphs, J. Graph Theory 24 (1997) 45-57, doi: 10.1002/(SICI)1097-0118(199701)24:1<45::AID-JGT6>3.0.CO;2-J
• [8] R. Thomas and P. Wollan, An Improved Edge Bound for Graph Linkages, preprint.
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Bibliografia
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