Geodesic
A SUFFICIENT CONDITION FOR A GRAPH TO BE A FRACTIONAL (f, n)-CRITICAL GRAPH
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 409-415

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Let a, b and n be non-negative integers such that 1 ≤ a ≤ b, and let G be a graph of order p with and f be an integer-valued function defined on V(G) such that a ≤ f(x) ≤ b for all x ∈ V(G). Let h: E(G) → [0, 1] be a function. If ∑e∋xh(e) = f(x) holds for any x ∈ V(G), then we call G[Fh] a fractional f-factor of G with indicator function h, where Fh = {e ∈ E(G): h(e) > 0}. A graph G is called a fractional (f, n)-critical graph if after deleting any n vertices of G the remaining graph of G has a fractional f-factor. In this paper, it is proved that G is a fractional (f, n)-critical graph if for every non-empty independent subset X of V(G), and . Furthermore, it is shown that the result in this paper is best possible in some sense.
DOI : 10.1017/S001708951000011X
Mots-clés : 05C70 
ZHOU, SIZHONG. A SUFFICIENT CONDITION FOR A GRAPH TO BE A FRACTIONAL (f, n)-CRITICAL GRAPH. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 409-415. doi: 10.1017/S001708951000011X
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     title = {A {SUFFICIENT} {CONDITION} {FOR} {A} {GRAPH} {TO} {BE} {A} {FRACTIONAL} (f, {n)-CRITICAL} {GRAPH}},
     journal = {Glasgow mathematical journal},
     pages = {409--415},
     year = {2010},
     volume = {52},
     number = {2},
     doi = {10.1017/S001708951000011X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951000011X/}
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