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2007 | 27 | 3 | 507-526
Tytuł artykułu

The structure and existence of 2-factors in iterated line graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove several results about the structure of 2-factors in iterated line graphs. Specifically, we give degree conditions on G that ensure L²(G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L²(G) with all cycle lengths specified. We also give a characterization of the graphs G where $L^k(G)$ contains a 2-factor.
Słowa kluczowe
Wydawca
Rocznik
Tom
27
Numer
3
Strony
507-526
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-07-27
poprawiono
2007-03-02
zaakceptowano
2007-03-02
Twórcy
  • Department of Theoretical and Applied Mathematics, The University of Akron, Akron, OH 44325, USA
  • Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
  • Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA
Bibliografia
  • [1] J.A. Bondy, Pancyclic graphs, I, J. Combin. Theory (B) 11 (1971) 80-84, doi: 10.1016/0095-8956(71)90016-5.
  • [2] G. Chartrand, The existence of complete cycles in repeated line-graphs, Bull. Amer. Math. Society 71 (1965) 668-670, doi: 10.1090/S0002-9904-1965-11389-1.
  • [3] M.H. El-Zahar, On circuits in graphs, Discrete Math. 50 (1984) 227-230, doi: 10.1016/0012-365X(84)90050-5.
  • [4] R.J. Gould, Advances on the hamiltonian problem-a survey, Graphs Combin. 19 (2003) 7-52, doi: 10.1007/s00373-002-0492-x.
  • [5] R.J. Gould and E.A. Hynds, A note on cycles in 2-factors of line graphs, Bull. of the ICA 26 (1999) 46-48.
  • [6] F. Harary and C.St.J.A. Nash-Williams, On eulerian and hamiltonian graphs and line graphs, Canad. Math. Bull. 8 (1965) 701-709, doi: 10.4153/CMB-1965-051-3.
  • [7] S.G. Hartke and A.W. Higgins, Minimum degree growth of the iterated line graph, Ars Combin. 69 (2003) 275-283.
  • [8] S.G. Hartke and K. Ponto, k-Ordered hamiltonicity of iterated line graphs, preprint.
  • [9] M. Knor and L'. Niepel, Distance independent domination in iterated line graphs, Ars Combin. 79 (2006) 161-170.
  • [10] M. Knor and L'. Niepel, Iterated Line Graphs are Maximally Ordered, J. Graph Theory 52 (2006) 171-180, doi: 10.1002/jgt.20152.
  • [11] Z. Liu and L. Xiong, Hamiltonian iterated line graphs, Discrete Math 256 (2002) 407-422, doi: 10.1016/S0012-365X(01)00442-3.
  • [12] V.D. Samodivkin, P-indices of graphs, Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 23 (1987) 165-172.
  • [13] D.B. West, Introduction to Graph Theory, 2nd ed. (Prentice Hall, Upper Saddle River, NJ, 2001).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1376
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