Connected factors in graphs -- a survey (Q1777234)

A subgraph \(F\) of a graph \(G\) is called a factor of \(G\) if \(V(F)= V(G)\) and \(E(F)\subseteq E(G)\). In other words \(F\) is a spanning subgraph of \(G\). A survey of factors of \(G\) that add additional restrictions on \(F\) are studied in this paper. For example, if \(f\) is a function from \(V(G)\) into the nonnegative integers, then \(F\) is called an \(f\)-factor if \(\deg F(v)= f(v)\) for all \(v\) in \(V(G)\). So, factors may be selected by degree properties. Factors may also be selected by some structural properties. Some of the earliest results of graph theory on Hamiltonian cycles, spanning trees and walks fall naturally in that category. This survey considers many results about various factors of graphs. It is a complete up-to-date survey of factors and factorizations.