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2004 | 24 | 1 | 23-40
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Hamilton cycles in split graphs with large minimum degree

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A graph G is called a split graph if the vertex-set V of G can be partitioned into two subsets V₁ and V₂ such that the subgraphs of G induced by V₁ and V₂ are empty and complete, respectively. In this paper, we characterize hamiltonian graphs in the class of split graphs with minimum degree δ at least |V₁| - 2.
Słowa kluczowe
Wydawca
Rocznik
Tom
24
Numer
1
Strony
23-40
Opis fizyczny
Daty
wydano
2004
otrzymano
2001-02-13
poprawiono
2002-10-02
Twórcy
autor
  • Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Vietnam
autor
  • Provincial Office of Education and Training, Tuyen Quang, Vietnam
Bibliografia
  • [1] M. Behzad and G. Chartrand, Introduction to the theory of graphs (Allyn and Bacon, Boston, 1971).
  • [2] R.E. Burkard and P.L. Hammer, A note on hamiltonian split graphs, J. Combin. Theory 28 (1980) 245-248, doi: 10.1016/0095-8956(80)90069-6.
  • [3] V. Chvatal, New directions in hamiltonian graph theory, in: New directions in the theory of graphs (Proc. Third Ann Arbor Conf. Graph Theory, Univ. Michigan, Ann Arbor, Mich., 1971), pp. 65-95, Acad. Press, NY 1973.
  • [4] V. Chvatal and P. Erdős, A note on hamiltonian circiuts, Discrete Math. 2 (1972) 111-113, doi: 10.1016/0012-365X(72)90079-9.
  • [5] V. Chvatal and P.L. Hammer, Aggregation of inequalities in integer programming, Ann. Discrete Math. 1 (1977) 145-162, doi: 10.1016/S0167-5060(08)70731-3.
  • [6] S. Foldes, P.L. Hammer, Split graphs, in: Proceedings of the Eighth Southeastern conference on Combinatorics, Graph Theory and Computing (Louisiana State Univ., Baton Rouge, La., 1977), 311-315. Congressus Numerantium, No XIX, Utilitas Math., Winnipeg, Man., 1977.
  • [7] S. Foldes and P.L. Hammer, On a class of matroid-producing graphs, in: Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely 1976) Vol. 1, 331-352, Colloq. Math. Soc. Janós Bolyai, 18 (North-Holland, Amsterdam-New York, 1978).
  • [8] R.J. Gould, Updating the hamiltonian problem, a survey, J. Graph Theory 15 (1991) 121-157, doi: 10.1002/jgt.3190150204.
  • [9] P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935) 26-30, doi: 10.1112/jlms/s1-10.37.26.
  • [10] F. Harary and U. Peled, Hamiltonian threshold graphs, Discrete Appl. Math. 16 (1987) 11-15, doi: 10.1016/0166-218X(87)90050-3.
  • [11] B. Jackson and O. Ordaz, Chvatal-Erdős conditions for paths and cycles in graphs and digraphs, a survey, Discrete Math. 84 (1990) 241-254, doi: 10.1016/0012-365X(90)90130-A.
  • [12] J. Peemöller, Necessary conditions for hamiltonian split graphs, Discrete Math. 54 (1985) 39-47.
  • [13] U.N. Peled, Regular Boolean functions and their polytope, Chapter VI (Ph. D. Thesis, Univ. of Waterloo, Dep. Combin. and Optimization, 1975).
  • [14] S.B. Rao, Solution of the hamiltonian problem for self-complementary graphs, J. Combin. Theory (B) 27 (1979) 13-41, doi: 10.1016/0095-8956(79)90065-0.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1210
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