Tutte's f-factor theorem can be stated as follows. Theorem B [16] (but see [17]) A graph G has an f-factor if and only if, for each pair of disjoint subsets S, T of V (G), odd(Gf − XS,T ) ≤ |XS,T |. G such that dF (v) = f(v) for each v in V (G).
Nov 15, 2023
Let m, l, n be three odd integers such that m > l > n. It is proved that if a graph G has an m-factor and an n-factor, then it also has an l-factor.
Given a function f: V(G) + N = (0, 1,2, . . .}, we say that G has anf-factor if there exists a spanning subgraph H of G such that d&) = f(x) for every x E V(G).
Oct 22, 2024 · A (g, f)-factor of a graph is a subset F of E such that for all v is an element of V, g(v) <= deg(F)(V) <= f(v). Lovasz gave a necessary and ...
In this paper, we give sufficient conditions for a graph to have an f-factor and a. (g, f)-factor that contain given edges or do not contain given edges. For ...
Katerinis [1] showed a sufficient condition for the existence of an f-factor in terms of vertex-deleted subgraphs. Theorem. A (Katerinis. [1]). Let G be a graph ...
(ii) If P is a hereditary property, then P2(G, f) is necessary for P(G, f). Therefore P2 is a necessary condition for the existence of a perfect f-factor.
Jan 27, 2021 · Theorem 5. A graph G is said to be a fractional (g, f)-covered graph if for any e ∈ E(G), there exists a fractional (g, f)-factor Fh ...
In this paper, we give a necessary and sufficient condition for a bipartite graph to have an f-factor containing a set of edges and excluding another set of ...
Conjugation is controlled by an episome called the F factor. The time it takes for individual genes to be transferred during conjugation provides information ...
Missing: conditions | Show results with:conditions