PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 34 | 2 | 287-307
Tytuł artykułu

Heavy subgraph pairs for traceability of block-chains

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A graph is called traceable if it contains a Hamilton path, i.e., a path containing all its vertices. Let G be a graph on n vertices. We say that an induced subgraph of G is o−1-heavy if it contains two nonadjacent vertices which satisfy an Ore-type degree condition for traceability, i.e., with degree sum at least n−1 in G. A block-chain is a graph whose block graph is a path, i.e., it is either a P1, P2, or a 2-connected graph, or a graph with at least one cut vertex and exactly two end-blocks. Obviously, every traceable graph is a block-chain, but the reverse does not hold. In this paper we characterize all the pairs of connected o−1-heavy graphs that guarantee traceability of block-chains. Our main result is a common extension of earlier work on degree sum conditions, forbidden subgraph conditions and heavy subgraph conditions for traceability
Wydawca
Rocznik
Tom
34
Numer
2
Strony
287-307
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-04-12
Twórcy
autor
  • Department of Applied Mathematics Northwestern Polytechnical University Xi’an, Shaanxi 710072, P.R. China
  • Faculty of EEMCS, University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands
  • Department of Applied Mathematics Northwestern Polytechnical University Xi’an, Shaanxi 710072, P.R. China
Bibliografia
  • [1] P. Bedrossian, G. Chen, and R.H. Schelp, A generalization of Fan’s condition for hamiltonicity, pancyclicity, and hamiltonian connectedness, Discrete Math. 115 (1993) 39-50. doi:10.1016/0012-365X(93)90476-A[Crossref]
  • [2] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer Graduate Texts in Mathe- matics 244 (2008).
  • [3] H.J. Broersma, Z. Ryj´aˇcek and I. Schiermeyer, Dirac’s minimum degree condition restricted to claws, Discrete Math. 167/168 (1997) 155-166. doi:10.1016/S0012-365X(96)00224-5[Crossref]
  • [4] H.J. Broersma and H.J. Veldman, Restrictions on induced subgraphs ensuring hamil- tonicity or pancyclicity of K1,3-free graphs, in: R. Bodendiek (Ed.) Contemporary Methods in Graph Theory, (BI Wissenschaftsverlag, Mannheim-Wien-Zfirich, 1990) 181-194.
  • [5] R. Čada, Degree conditions on induced claws, Discrete Math. 308 (2008) 5622-5631. doi:10.1016/j.disc.2007.10.026[Crossref][WoS]
  • [6] D. Duffus, R.J. Gould and M.S. Jacobson, Forbidden subgraphs and the hamiltonian theme, in: The Theory and Applications of Graphs (Kalamazoo, Mich. 1980, Wiley, New York, 1981) 297-316.
  • [7] R.J. Faudree and R.J. Gould, Characterizing forbidden pairs for Hamiltonian prop- erties, Discrete Math. 173 (1997) 45-60. doi:10.1016/S0012-365X(96)00147-1[Crossref]
  • [8] H. Fleischner, The square of every two-connected graph is hamiltonian, J. Combin. Theory (B) 16 (1974) 29-34. doi:10.1016/0095-8956(74)90091-4[Crossref]
  • [9] B. Li, H.J. Broersma and S. Zhang, Forbidden subgraph pairs for traceability of block-chains, Electron. J. Graph Theory Appl. 1 (2013) 1-10.
  • [10] B. Li, Z. Ryjáček, Y.Wang and S. Zhang, Pairs of heavy subgraphs for Hamiltonicity of 2-connected graphs, SIAM J. Discrete Math. 26 (2012) 1088-1103. doi:10.1137/11084786X[WoS]
  • [11] B. Li and S. Zhang, On traceability of claw-o−1-heavy graphs (2013). arXiv:1303.0991v1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1737
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.