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

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

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## Abstract

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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 ≤ ∑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.

## How to cite

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Sizhong 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--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--factor-critical graph
UR - http://eudml.org/doc/277129
ER -

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