# A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

Sizhong Zhou; Fan Yang; Zhiren Sun

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 2, page 409-418
- ISSN: 2083-5892

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topSizhong Zhou, Fan Yang, and Zhiren Sun. "A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 409-418. <http://eudml.org/doc/277129>.

@article{SizhongZhou2016,

abstract = {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 ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = \{e ∈ E(G) : h(e) > 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 [...] 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.},

author = {Sizhong Zhou, Fan Yang, Zhiren Sun},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; minimum degree; neighborhood; fractional [a; b]-factor; fractional ID-[a; b]-factor-critical graph; fractional -factor; fractional $ID-[a, b]$-factor-critical graph},

language = {eng},

number = {2},

pages = {409-418},

title = {A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs},

url = {http://eudml.org/doc/277129},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Sizhong Zhou

AU - Fan Yang

AU - Zhiren Sun

TI - A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2016

VL - 36

IS - 2

SP - 409

EP - 418

AB - 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 ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 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 [...] 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.

LA - eng

KW - graph; minimum degree; neighborhood; fractional [a; b]-factor; fractional ID-[a; b]-factor-critical graph; fractional -factor; fractional $ID-[a, b]$-factor-critical graph

UR - http://eudml.org/doc/277129

ER -

## References

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- [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. Zbl1260.05119
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