A neighborhood condition for fractional ID-[a, b]-factor-critical graphs
نویسندگان
چکیده
A graph G is fractional ID-[a, b]-factor-critical if G − I has a fractional [a, b]-factor for every independent set I of G. We extend a result of Zhou and Sun concerning fractional ID-k-factor-critical graphs.
منابع مشابه
A 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 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 کاملDegree 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 NEIGHBORHOOD UNION CONDITION FOR FRACTIONAL (k, n′,m)-CRITICAL DELETED GRAPHS
A graph G is called a fractional (k, n′,m)-critical deleted graph if any n′ vertices are removed from G the resulting graph is a fractional (k,m)-deleted graph. In this paper, we prove that for integers k ≥ 2, n′,m ≥ 0, n ≥ 8k + n′ + 4m− 7, and δ(G) ≥ k + n′ +m, if |NG(x) ∪NG(y)| ≥ n+ n′ 2 for each pair of non-adjacent vertices x, y of G, then G is a fractional (k, n′,m)-critical deleted graph....
متن کاملIndependent Set Neighborhood Union And Fractional Critical Deleted Graphs∗
A graph G is called a fractional (k, n′,m)-critical deleted graph if any n′ vertices are removed from G the resulting graph is a fractional (k,m)-deleted graph. In this paper, we determine that for integers k ≥ 1, i ≥ 2, n′,m ≥ 0, n > 4ki+ n′ + 4m− 4, and δ(G) ≥ k(i− 1) + n′ + 2m, if |NG(x1) ∪NG(x2) ∪ · · · ∪NG(xi)| ≥ n+ n′ 2 for any independent subset {x1, x2, . . . , xi} of V (G), then G is a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 36 شماره
صفحات -
تاریخ انتشار 2016