Independent Set Neighborhood Union And Fractional Critical Deleted Graphs∗
نویسندگان
چکیده
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 fractional (k, n′,m)critical deleted graph. The bound for independent set neighborhood union condition is sharp.
منابع مشابه
A 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....
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