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Języki publikacji
Abstrakty
A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order 2n obtained from the complete balanced bipartite Kn,n by removing at most n - 2 edges, is bipancyclic. We prove an analogous result for balanced tripartite graphs: If G is a balanced tripartite graph of order 3n and size at least 3n(2) - 2n + 2, then G contains cycles of all lengths.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
337--343
Opis fizyczny
Bibliogr. 5 poz., rys.
Twórcy
autor
- The University of Western Ontario, Department of Mathematics, London, Ontario N6A 5B7 Canada, jadamus@uwo.ca
Bibliografia
- [1] J.A. Bondy, Pancyclic graphs I, J. Combinatorial Theory B 11 (1971), 80–84.
- [2] G. Chen, R.J. Faudree, R.J. Gould, M.S. Jacobson, L. Lesniak, Hamiltonicity in balanced k-partite graphs, Graphs and Combinatorics 11 (1995), 221–231.
- [3] G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 3 (1952) 2, 69–81.
- [4] R.C. Entringer, E. Schmeichel, Edge conditions and cycle structure in bipartite graphs, Ars Combinatoria 26 (1988), 229–232.
- [5] K. Yokomura, A degree sum condition on hamiltonian cycles in balanced 3-partite graphs, Discrete Math. 178 (1998), 293–297.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0002-0001