Browse > Article
http://dx.doi.org/10.14317/jami.2016.435

BINDING NUMBERS AND FRACTIONAL (g, f, n)-CRITICAL GRAPHS  

ZHOU, SIZHONG (School of Mathematics and Physics, Jiangsu University of Science and Technology)
SUN, ZHIREN (School of Mathematical Sciences, Nanjing Normal University)
Publication Information
Journal of applied mathematics & informatics / v.34, no.5_6, 2016 , pp. 435-441 More about this Journal
Abstract
Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.
Keywords
graph; binding number; fractional (g, f)-factor; fractional (g, f, n)-critical graph;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, GTM-244, Berlin: Springer, 2008.
2 O. Fourtounelli and P. Katerinis, The existence of k-factors in squares of graphs, Discrete Math. 310 (2010), 3351-3358.   DOI
3 P. Katerinis and D.R. Woodall, Binding numbers of graphs and the existence of k-factors, Quart. J. Math. Oxford 38 (1987), 221-228.   DOI
4 K. Kimura, f-factors, complete-factors, and component-deleted subgraphs, Discrete Math. 313 (2013), 1452-1463.   DOI
5 M. Kouider and S. Ouatiki, Sufficient condition for the existence of an even [a, b]-factor in graph, Graphs Combin. 29 (2013), 1051-1057.   DOI
6 R. Kužel, K. Ozeki and K. Yoshimoto, 2-factors and independent sets on claw-free graphs, Discrete Math. 312 (2012), 202-206.   DOI
7 G. Liu and L. Zhang, Characterizations of maximum fractional (g, f)-factors of graphs, Discrete Appl. Math. 156 (2008), 2293-2299.   DOI
8 G. Liu and L. Zhang, Toughness and the existence of fractional k-factors of graphs, Discrete Math. 308 (2008), 1741-1748.   DOI
9 S. Liu, On toughness and fractional (g, f, n)-critical graphs, Inform. Process. Lett. 110 (2010), 378-382.   DOI
10 H. Lu, Regular graphs, eigenvalues and regular factors, J. Graph Theory 69 (2012), 349-355.   DOI
11 H. Lu, Simplified existence theorems on all fractional [a, b]-factors, Discrete Appl. Math. 161 (2013), 2075-2078.   DOI
12 D.R. Woodall, The binding number of a graph and its Anderson number, J. Combin. Theory ser. B 15 (1973), 225-255.   DOI
13 S. Zhou, A new neighborhood condition for graphs to be fractional (k,m)-deleted graphs, Appl. Math. Lett. 25 (2012), 509-513.   DOI
14 S. Zhou, Independence number, connectivity and (a, b, k)-critical graphs, Discrete Math. 309 (2009), 4144-4148.   DOI
15 S. Zhou and Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109 (2009), 811-815.   DOI
16 S. Zhou, Z. Sun and H. Ye, A toughness condition for fractional (k,m)-deleted graphs, Inform. Process. Lett. 113 (2013), 255-259.   DOI