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2016 | 57 | 404-415
Article title

Hamiltonian cycle containg selected sets of edges of a graph

Content
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Languages of publication
EN
Abstracts
EN
The aim of this paper is to characterize for every k ≥ 1 all (l + 3)-connected graphs G on n ≥ 3 vertices satisfying P(n + k): for each pair of vertices x and y in G, such that there is a path system S of length k with l internal vertices which components are paths of length at most 2 satisfying: such that S is not contained in any hamiltonian cycle of G.
Year
Volume
57
Pages
404-415
Physical description
Contributors
  • Institute of Mathematics, Tadeusz Kościuszko Cracow University of Technology, 24 Warszawska Str., 31-155 Cracow, Poland, gancarz@pk.edu.pl
References
  • [1] J. A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135.
  • [2] J. A. Bondy and U.S.R. Murty, Graph theory with applications, MacMillan Press LTD, 1976.
  • [3] G. Fan, New sufficient conditions for cycles in graphs, J. Combin. Theory Ser. B 37 (1984) 221-227.
  • [4] G. Gancarzewicz and A. P. Wojda, Graphs with every k-matching in a hamiltonian cycle, Discrete Math. 213(1-3) (2000) 141-151.
  • [5] H. V. Kronk, Variations of a theorem of pósa, in The Many Facets of Graph Theory, ed. G. Chartrand and S.F. Kapoor, Lect. Notes Math. 110 (1969) 193-197.
  • [6] O. Ore, Note on hamiltonian circuits, Amer. Math. Monthly 67 (1960) 55.
  • [7] Z. Skupień and A. P. Wojda, On highly hamiltonian graphs, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 22 (1974) 463-471.
  • [8] M. Las Vargnas, Sur une propriété des arbres maximaux dans un graphe, C. R. Axad. Sci. Paris, Sér. A 272 (1971) 1297-1300.
  • [9] A. P. Wojda, Hamiltonian cycles through matchings, Demonstratio Mathematica XXI(2) (1983) 547-553.
Document Type
article
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.psjd-77051fa1-8c40-466c-9628-02b2569aa3ec
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