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

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

A degree condition for the existence of connected factors

All under collsidfcration vertiCt~S x and y. We write II subsets X and Y of we denote and y functions defined on has a, rnatch·· is a connected t= GiVPll of G induc~'d to be the neighborhood of x. Let 1 and 9 be 1(v) _ g(v) dG(v) for aJl

Connected (g, f)-factors and supereulerian digraphs

Given a digraph (an undirected graph, resp.) D and two positive integers f (x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)-factor if g(x) d + H (x) = d ? H (x) f (x)(g(x) d H (x) f (x), resp.) for every x 2 V (D). If f (x) = g(x) = 1 for every x, then a connected (g; f)-factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for ...

Minimum Degree of Graphs and (g, f, n)-Critical Graphs

Let G be a graph of order p, and let a and b and n be nonnegative integers with 1 ≤ a ≤ b, and let g and f be two integer-valued functions defined on V (G) such that a ≤ g(x) ≤ f(x) ≤ b for all x ∈ V (G). A (g, f)-factor of graph G is defined as a spanning subgraph F of G such that g(x) ≤ dF (x) ≤ f(x) for each x ∈ V (G). Then a graph G is called a (g, f, n)-critical graph if after deleting any...

TIGHT TOUGHNESS CONDITION FOR FRACTIONAL (g, f, n)-CRITICAL GRAPHS

All graphs considered in this paper are finite, loopless, and without multiple edges. The notation and terminology used but undefined in this paper can be found in [2]. Let G be a graph with the vertex set V (G) and the edge set E(G). For a vertex x ∈ V (G), we use dG(x) and NG(x) to denote the degree and the neighborhood of x in G, respectively. Let δ(G) denote the minimum degree of G. For any...

Minimum Degree Conditions for Graphs to be (g, f, n)-Critical Graphs

Let G be a graph of order p, and let a and b and n be nonnegative integers with 1 ≤ a ≤ b, and let g and f be two integer-valued functions defined on V (G) such that a ≤ g(x) ≤ f(x) ≤ b for all x ∈ V (G). A (g, f)-factor of graph G is defined as a spanning subgraph F of G such that g(x) ≤ dF (x) ≤ f(x) for each x ∈ V (G). Then a graph G is called a (g, f, n)-critical graph if after deleting any...