**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31103

##### Notes on Fractional k-Covered Graphs

**Authors:**
Sizhong Zhou,
Yang Xu

**Abstract:**

**Keywords:**
graph,
fractional k-factor,
binding number,
fractional k-covered graph

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1085545

**References:**

[1] D.R. Woodall, The binding number of a graph and its Anderson number, J.Combin. Theory ser. B 15(1973), 225-255.

[2] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, London, The Macmillan Press, 1976.

[3] Edward R. Schinerman and D.H. Ullman, Fractional Graph Theory, John Wiley and Son. Inc. New York, 1997.

[4] S. Zhou, Independence number, connectivity and (a, b, k)-critical graphs, Discrete Mathematics 309(12)(2009), 4144-4148.

[5] S. Zhou, A new sufficient condition for graphs to be (g, f, n)-critical graphs, Canadian Mathematical Bulletin, to appear.

[6] S. Zhou, A sufficient condition for a graph to be an (a, b, k)-critical graph, International Journal of Computer Mathematics, to appear.

[7] S. Zhou and Y. Xu, Neighborhoods of independent sets for (a, b, k)- Critical Graphs, Bulletin of the Australian Mathematical Society 77(2)(2008), 277-283.

[8] G. Liu and L. Zhang, Fractional (g, f)-factors of graphs, Acta Math. Scientia (Ser. B) 21(4)(2001), 541-545.

[9] S. Zhou and Q. Shen, On fractional (f, n)-critical graphs, Information Processing Letters 109(14)(2009), 811-815.

[10] S. Zhou, Some results on fractional k-factors, Indian Journal of Pure and Applied Mathematics 40(2)(2009), 113-121.

[11] S. Zhou and H. Liu, Neighborhood conditions and fractional k-factors, Bulletin of the Malaysian Mathematical Sciences Society 32(1)(2009), 37-45.

[12] S. Zhou and C. Shang, Some sufficient conditions with fractional (g, f)-factors in graphs, Chinese Journal of Engineering Mathematics 24(2)(2007), 329-333.

[13] Z. Li, G. Yan and X. Zhang, On fractional f-covered graphs, OR Trasactions (in Chinese) 6(4)(2002), 65-68.

[14] Z. Li, G. Yan and X. Zhang, Isolated toughness and fractional k-covered graphs, Acta mathematicae Applicatae Sinica 27(4)(2004), 593-598.

[15] R. R. Anstee, An Algorithmic Proof Tutte-s f-Factor Theorem, J. Algorithms 6(1985), 112-131.