Let G be a graph of order n, and let be nonnegative integers with . An -factor of G is defined as a spanning subgraph F of G such that for each . If , then an -factor is called a k-factor. In this Note, it is proved that if G has a k-factor Q, , the binding number , and for any nonempty independent subset X of , then G has an -factor F such that .
Soit G un graphe dʼordre n et des entiers positifs tels que . Un -facteur est défini comme étant un sous-graphe couvrant F de G tel que pour tout . Si , alors un -facteur est appelé k-facteur. Dans cette Note on démontre que si G a un k-facteur , le nombre de liaisons et pour tout sous-ensemble X non vide indépendant de , alors G a un -facteur F tel que .
Accepted:
Published online:
Sizhong Zhou 1
@article{CRMATH_2011__349_19-20_1021_0, author = {Sizhong Zhou}, title = {Binding numbers and $ [a,b]$-factors excluding a given \protect\emph{k}-factor}, journal = {Comptes Rendus. Math\'ematique}, pages = {1021--1024}, publisher = {Elsevier}, volume = {349}, number = {19-20}, year = {2011}, doi = {10.1016/j.crma.2011.08.007}, language = {en}, }
Sizhong Zhou. Binding numbers and $ [a,b]$-factors excluding a given k-factor. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1021-1024. doi : 10.1016/j.crma.2011.08.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.007/
[1] Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1982
[2] Binding number and Hamiltonian -factors in graphs, J. Appl. Math. Comput., Volume 25 (2007), pp. 383-388
[3] The existence of k-factors in squares of graphs, Discrete Math., Volume 310 (2010), pp. 3351-3358
[4] Binding numbers of graphs and the existence of k-factors, Quart. J. Math. Oxford, Volume 38 (1987), pp. 221-228
[5] Degree conditions for graphs to have -factors excluding a given k-factor, J. Sys. Sci. & Math. Sci., Volume 29 (2009), pp. 1052-1060
[6] Subgraphs with prescribed valencies, J. Combin. Theory, Volume 8 (1970), pp. 391-416
[7] Fan-type results for the existence of -factors, Discrete Math., Volume 306 (2006), pp. 688-693
[8] The binding number of a graph and its Anderson number, J. Combin. Theory Ser. B, Volume 15 (1973), pp. 225-255
[9] Independence number, connectivity and -critical graphs, Discrete Math., Volume 309 (2009), pp. 4144-4148
[10] Notes on the binding numbers for -critical graphs, Bull. Aust. Math. Soc., Volume 76 (2007), pp. 307-314
[11] Toughness and -critical graphs, Inform. Process. Lett., Volume 111 (2011), pp. 403-407
Cited by Sources:
☆ This research was supported by Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (10KJB110003) and Jiangsu University of Science and Technology (2010SL101J, 2009SL154J), and was sponsored by Qing Lan Project of Jiangsu Province.
Comments - Policy