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2004 | 24 | 1 | 55-71
Tytuł artykułu

On traceability and 2-factors in claw-free graphs

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
If G is a claw-free graph of sufficiently large order n, satisfying a degree condition σₖ > n + k² - 4k + 7 (where k is an arbitrary constant), then G has a 2-factor with at most k - 1 components. As a second main result, we present classes of graphs 𝓒₁,...,𝓒₈ such that every sufficiently large connected claw-free graph satisfying degree condition σ₆(k) > n + 19 (or, as a corollary, δ(G) > (n+19)/6) either belongs to $⋃ ⁸_{i=1} 𝓒_i$ or is traceable.
Słowa kluczowe
Wydawca
Rocznik
Tom
24
Numer
1
Strony
55-71
Opis fizyczny
Daty
wydano
2004
otrzymano
2001-05-29
poprawiono
2002-11-14
Twórcy
  • Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN 55810, U.S.A.
  • Department of Applied Mathematics, Technical University of Ostrava, Ostrava, Czech Republic
  • Department of Mathematics, University of West Bohemia
  • Institute of Theoretical Computer Science, Charles University, Univerzitní 8, 306 14 Plzeň, Czech Republic
  • Faculty of Applied Mathematics, University of Mining and Metallurgy AGH, al. Mickiewicza 30, 30-059 Kraków, Poland
Bibliografia
  • [1] J.A. Bondy and U.S.R. Murty, Graph Theory with applications (Macmillan, London and Elsevier, New York, 1976).
  • [2] V. Chvátal and P. Erdős, A note on hamiltonian circuits, Discrete Math. 2 (1972) 111-113, doi: 10.1016/0012-365X(72)90079-9.
  • [3] S. Brandt, O. Favaron and Z. Ryjáček, Closure and stable hamiltonian properties in claw-free graphs, J. Graph Theory 32 (2000) 30-41, doi: 10.1002/(SICI)1097-0118(200005)34:1<30::AID-JGT4>3.0.CO;2-R
  • [4] G.A. Dirac, In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen, Math. Nachr. 22 (1960) 61-85, doi: 10.1002/mana.19600220107.
  • [5] R. Faudree, O. Favaron, E. Flandrin, H. Li and Z.Liu, On 2-factors in claw-free graphs, Discrete Math. 206 (1999) 131-137, doi: 10.1016/S0012-365X(98)00398-7.
  • [6] O. Favaron, E. Flandrin, H. Li and Z. Ryjáček, Clique covering and degree conditions for hamiltonicity in claw-free graphs, Discrete Math. 236 (2001) 65-80, doi: 10.1016/S0012-365X(00)00432-5.
  • [7] R.L. Graham, M. Grötschel and L. Lovász, eds., (Handbook of Combinatorics. North-Holland, 1995).
  • [8] R. Gould and M. Jacobson, Two-factors with few cycles in claw-free graphs, preprint 1999.
  • [9] O. Kovárík, M. Mulac and Z. Ryjáček, A note on degree conditions for hamiltonicity in 2-connected claw-free graphs, Discrete Math. 244 (2002) 253-268, doi: 10.1016/S0012-365X(01)00088-7.
  • [10] H. Li, A note on hamiltonian claw-free graphs, Rapport de Recherche LRI No. 1022 (Univ. de Paris-Sud, 1996), submitted.
  • [11] 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.
  • [12] Z. Ryjáček, On a closure concept in claw-free graphs, J. Combin. Theory (B) 70 (1997) 217-224, doi: 10.1006/jctb.1996.1732.
  • [13] Z. Ryjáček, A. Saito and R.H. Schelp, Closure, 2-factors and cycle coverings in claw-free graphs, J. Graph Theory 32 (1999) 109-117, doi: 10.1002/(SICI)1097-0118(199910)32:2<109::AID-JGT1>3.0.CO;2-O
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1213
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