A Neighborhood Condition for Graphs to Have Special [a,b]-Factor

A Degree Condition For Graphs to Have Connected (g, f)-Factors

A Neighborhood Condition for Graphs to Have [ a , b ]-Factors III

Let a, b, k, and m be positive integers such that 1 ≤ a < b and 2 ≤ k ≤ (b + 1− m)/a. Let G = (V (G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b − 1) − 1)/b and |NG(x1) ∪ NG(x2) ∪ · · · ∪ NG(xk)| ≥ a|G|/(a+ b) for every independent set {x1, x2, . . . , xk} ⊆ V (G). Then for any subgraph H of G with m edges and δ(G−E(H)) ≥ a, G has an [a, b]-factor F such that E(H) ∩ E(F )...

a degree condition for graphs to have connected (g, f)-factors

A neighborhood condition for fractional ID-[a, b]-factor-critical graphs

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.

A neighborhood condition for fractional k-deleted graphs

Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k + 3− 4 √ 2(k − 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G ...