Abstract
LetG be a graph of ordern ≥ 6 with minimum degree at least ⌈(n + 1)/2⌉. Then, for any two integerss andt withs ≥ 3,t ≥ 3 ands + t ≤ n, G contains two vertex-disjoint cycles of lengthss andt, respectively, unless thatn, s andt are odd andG is isomorphic toK (n−1)/2,(n−1)/2 + K1. We also show that ifG is a graph of ordern ≥ 8 withn even and minimum degree at leastn/2, thenG contains two vertex-disjoint cycles with any given even lengths provided that the sum of the two lengths is at mostn.
Similar content being viewed by others
References
Bollobá, B.: Extremal Graph Theory, Academic Press, London (1978)
Bondy, J.: Pancyclic graphs I. J. Comb. Theory(B), 11, 80–84 (1971)
Bondy, J., Chvátal, V.: A method in graph theory. Discrete Math.15, 111–135 (1976)
Dirac, G.A.: Some theorems on abstract graphs. Proc. London Math. Soc.2, 69–81 (1952)
El-Zahar, M.H.: On circuits in graphs. Discrete Math.50, 227–230 (1984)
Erdös, P., Gallai, T.: On maximal paths and circuits of graphs. Acta Math. Acad. Sci. Hungar.10, 337–356 (1959)
Ore, O.: Note on Hamilton circuits. Amer. Math. Monthly,67, 55 (1960)
Wang, H.: Partition of a bipartite graph into cycles. Discrete Math.117, 287–291 (1993)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, H. Two vertex-disjoint cycles in a graph. Graphs and Combinatorics 11, 389–396 (1995). https://doi.org/10.1007/BF01787818
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01787818