Abstract
We investigate relations of the minimum degree and the independence number of a simple graph for the existence of regular factors.
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Bauer, D., Schmeichel, E.: Toughness, minimum degree and the existence of 2-factors. J. Graph Theory.18, 241–256 (1994)
Bauer, D., Broersma, H.J., van den Heuvel, J., Veldman, H.J.: Long cycles in graphs with prescribed toughness and minimum degree. Discrete Math. (to be published)
Belck, H.-B.: Reguläre Faktoren von Graphen. J. Reine Angew. Math.188, 228–252 (1950)
Chvátal, V., Erdös, P.: A note on hamiltonian circuits. Discrete Math.2, 111–113 (1972)
Egawa, Y., Enomoto, H.: Sufficient conditions for the existence ofk-factors. In: Recent Studies in Graph Theory (V.R. Kulli, ed.), Vishwa International Publications, India (1989), 96–105
Enomoto, H.: Toughness and the existence ofk-factors II. Graphs and Combinatorics2, 37–42 (1986)
Enomoto, H., Jackson, B., Katernis, P., Saito, A.: Toughness and the existence ofk-factors, J. Graph Theory9, 87–95 (1985)
Iida, T., Nishimura, T.: An Ore-type condition for the existence ofk-factors in graphs. Graphs and Combinatorics7, 353–361 (1991)
Katerinis, P.: Minimum degree of a graph and the existence ofk-factors. Proc. Indian Acad. Sci. (Math. Sci.)94, 123–127 (1985)
Katerinis, P.: A Chvátal-Erdös condition for anr-factor in a graph. Ars Combinat.20-B, 185–191 (1985)
Katerinis, P., Woodall, D.R.: Binding numbers and the existence ofk-factors. Quart. J. Math. Oxford (2),38, 221–228 (1987)
Lenkewitz, U., Volkmann, L.: Neighborhood and degree conditions for the existence of regular factors. Ars Combinat. (to be published)
Nash-Williams, C.St.J.A.: Edge-disjoint hamiltonian circuits in graphs with vertices of large valency. In: Studies in Pure Mathematics (L. Mirsky, ed.) Academic Press, London, (1971), 157–183
Niessen, T.: Nash-Williams conditions and the existence ofk-factors. Ars Combinat.34, 251–256 (1992)
Niessen, T.: Neighborhood unions and regular factors, J. Graph Theory.19, 45–64 (1995)
Niessen, T.: Complete closure and regular factors. J. Combinat. Math. Combinat. Comput. (to be published)
Nishimura, T.: Independence number, connectivity, andr-factors. J. Graph Theory13, 63–69 (1989)
Nishimura, T.: A degree condition for the existence ofk-factors. J. Graph Theory15, 141–151 (1992)
Tokushige, N.: Binding number and minimum degree fork-factors. J. Graph Theory13, 607–617 (1989)
Tutte, W.T.: The factorization of linear graphs. J. London Math. Soc.4, 107–111 (1947)
Tutte, W.T.: The factors of graphs. Can. J. Math.,4, 314–328 (1952)
Tutte, W.T.: Spanning subgraphs with specified valencies. Discrete Math.9, 97–108 (1974)
Tutte, W.T.: The subgraph problem. Annals of Discrete Math.3, 289–295 (1978)
Wei, V.K.: Coding for a multiple access channel. Ph. D. Thesis, University of Hawai, Honolulu (1980)
Woodall, D.R.:k-factors and neighbourhoods of independent sets in graphs. J. London Math. Soc. (2)41, 385–392 (1990)
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Niessen, T. Minimum degree, independence number and regular factors. Graphs and Combinatorics 11, 367–378 (1995). https://doi.org/10.1007/BF01787816
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DOI: https://doi.org/10.1007/BF01787816