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Operations Research Transactions >

2016 , Vol. 20 >Issue 1: 125 - 130

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.013

Some results on fractional k-factor-critical graphs and fractional k-extendable graphs

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  • 1.  School of Mathematical Science, South China Normal University, Guangzhou 510631, China

Received date: 2015-05-28

  Online published: 2016-03-15

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Abstract

 A simple graph G is said to be fractional k-factor-critical if after deleting any k vertices, the remaining subgraph still has a fractional perfect matching. A graph G is called a fractional k-extendable graph if G has a fractional perfect matching containing M for any k-matching M. In this paper, a sufficient condition for a graph to be fractional k-factor-critical graph and fractional k-extendable graph is given, respectively. Besides, a sufficient and necessary condition for a graph to be fractional k-factor-critical graph is given.

Key words： fractional perfect matching; fractional k-factor-critical; fractional k-extendable; fractional matching number

Cite this article

HUANG Xiaoxian, LIU Yan, WU Bosi . Some results on fractional k-factor-critical graphs and fractional k-extendable graphs[J]. Operations Research Transactions, 2016 , 20(1) : 125 -130 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.013

References

[1] 李巧, 刘岩. 分数k-因子临界图的条件 [J]. 运筹学学报, 2013, 17(4): 123-130.
[2] Scheinerman E R, Ullman D H. Fractional Graph Theory [M]. New York: Wiley, 1997.
[3] Liu Y, Liu G Z. The fractional matching numbers of graphs [J]. Networks, 2002, 40(4): 228-231.
[4] Yu J G, Bian Q J, Wang N. Some results on fractional n-factor-critical graphs [J].  Journal of Applied Mathematics and Computing, 2007, 25(1-2): 283-291.
[5] Yang J B, Ma Y H, Liu G Z. Fractional (g,f)-factors in graphs [J]. Applied Mathematics a Journal of Chinese Universities, 2001, 16(4): 385-390.
[6] Ma Y H, Liu G Z. Isolated toughness and existence of fractional factors in graphs [J]. Acta Mathematicae Applicatae Sinica, 2003, 26(1): 133-140.
[7] Qi F. The study of fractional (k,n)-critical graphs and the correlative properties [D]. Jinan: Shandong Normal University, 2008.

 
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