A neighborhood condition for graphs to have [a,b]-factors

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 Sufficient Condition for Graphs to Have Hamiltonian [a, b]-Factors

Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2) b−2 . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1 a+b−3 for every nonempty independent subset X of V (G) and δ(G) > (a−1)n+a+b−4 a+...

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 ...