Geodesic
A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 409-418.

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Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤Σ_ e ∋ x h(e) ≤ b holds for any x ∈ V (G), then we call G[F_h] a fractional [a, b]-factor of G with indicator function h, where F_h = { e ∈ E(G) : h(e) gt; 0 }. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]-factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if n ≥(a+2b)(2a+2b-3)+1/b, δ (G) ≥bn/a+2b + a and | N_G(x) ∪ N_G(y) | ≥(a+b)n/a+2b for any two nonadjacent vertices x, y ∈ V (G), then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that this result is best possible in some sense.
Keywords: graph, minimum degree, neighborhood, fractional [a, b]-factor, fractional ID-[a, b]-factor-critical graph 
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Zhou, Sizhong; Yang, Fan; Sun, Zhiren. A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 2, pp. 409-418. http://geodesic.mathdoc.fr/item/DMGT_2016_36_2_a11/

[1] S. Zhou, Z. Sun and H. Liu, A minimum degree condition for fractional ID-[a, b]- factor-critical graphs, Bull. Aust. Math. Soc. 86 (2012) 177-183. doi:10.1017/S0004972711003467

[2] H. Matsuda, A neighborhood condition for graphs to have [a, b]-factors, Discrete Math. 224 (2000) 289-292. doi:10.1016/S0012-365X(00)00140-0

[3] J. Ekstein, P. Holub, T. Kaiser, L. Xiong and S. Zhang, Star subdivisions and con- nected even factors in the square of a graph, Discrete Math. 312 (2012) 2574-2578. doi:10.1016/j.disc.2011.09.004

[4] H. Lu, Simplified existence theorems on all fractional [a, b]-factors, Discrete Appl. Math. 161 (2013) 2075-2078. doi:10.1016/j.dam.2013.02.006

[5] S. Zhou, Independence number, connectivity and (a, b, k)-critical graphs, Discrete Math. 309 (2009) 4144-4148. doi:10.1016/j.disc.2008.12.013

[6] S. Zhou, A sufficient condition for graphs to be fractional (k,m)-deleted graphs, Appl. Math. Lett. 24 (2011) 1533-1538. doi:10.1016/j.aml.2011.03.041

[7] S. Zhou and H. Liu, Neighborhood conditions and fractional k-factors, Bull. Malays. Math. Sci. Soc. 32 (2009) 37-45.

[8] K. Kimura, f-factors, complete-factors, and component-deleted subgraphs, Discrete Math. 313 (2013) 1452-1463. doi:10.1016/j.disc.2013.03.009

[9] M. Kouider and Z. Lonc, Stability number and [a, b]-factors in graphs, J. Graph Theory 46 (2004) 254-264. doi:10.1002/jgt.20008

[10] R. Chang, G. Liu and Y. Zhu, Degree conditions of fractional ID-k-factor-critical graphs, Bull. Malays. Math. Sci. Soc. 33 (2010) 355-360.

[11] S. Zhou, Q. Bian and J. Wu, A result on fractional ID-k-factor-critical graphs, J. Combin. Math. Combin. Comput. 87 (2013) 229-236.

[12] S. Zhou, Binding numbers for fractional ID-k-factor-critical graphs, Acta Math. Sin. Engl. Ser. 30 (2014) 181-186. doi:10.1007/s10114-013-1396-9

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