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.
@article{bwmeta1.element.doi-10_7151_dmgt_1864,
author = {Sizhong Zhou and Fan Yang and Zhiren Sun},
title = {A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {409-418},
zbl = {1338.05220},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1864}
}
Sizhong Zhou; Fan Yang; Zhiren Sun. A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 409-418. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1864/