Sharp conditions on fractional ID-(<i>g</i>, <i>f</i>)-factor-critical covered graphs
نویسندگان
چکیده
Combining the concept of a fractional ( g , f )-covered graph with that ID-( )-factor-critical graph, we define covered graph. This paper reveals relationship between some parameters and existence graphs. A sufficient condition for being is presented. In addition, demonstrate sharpness main result in this by constructing special class. Furthermore, other parameters(such as binding number, toughness, sun toughness neighborhood union) graphs can be studied further.
منابع مشابه
Degree Conditions of Fractional ID-k-Factor-Critical Graphs
We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if G− I has a fractional k-factor for every independent set I of G. Some sufficient conditions for a graph to be fractional ID-k-factor-critical are studied in this paper. Furthermore, we show that the result is best possible in some sense. 2010 Mathematics Subject C...
متن کاملA result on fractional ID-[a, b]-factor-critical graphs
A graphG is fractional ID-[a, b]-factor-critical ifG−I includes a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved that if α(G) ≤ 4b(δ(G)−a+1) (a+1)2+4b , then G is fractional ID-[a, b]-factor-critical. Furthermore, it is shown that the result is best possible in some sense.
متن کاملSome Results on Fractional Covered Graphs∗
Let G = (V (G),E(G)) be a graph. and let g, f be two integer-valued functions defined on V (G) such that g(x)≤ f (x) for all x ∈V (G). G is called fractional (g, f )-covered if each edge e of G belongs to a fractional (g, f )-factor Gh such that h(e) = 1, where h is the indicator function of Gh. In this paper, sufficient conditions related to toughness and isolated toughness for a graph to be f...
متن کاملNotes on Fractional k-Covered Graphs
A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{ |NG(X)| |X| : Ø = X ⊆ V (G), NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5...
متن کاملA degree condition for graphs to be fractional ID-[a, b]-factor-critical
Let G be a graph of sufficiently large order n, and let a and b be integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑x∈e h(e) ≤ b holds for any x ∈ V (G), then G[Fh] is called 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 (simply, fractional ID-[a, b]-facto...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rairo-operations Research
سال: 2022
ISSN: ['1290-3868', '0399-0559']
DOI: https://doi.org/10.1051/ro/2022144