Factors and Factorizations of Graphs pp 193-218 | Cite as

# [*a, b*]-Factorizations

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## Abstract

Let *G* be a graph, and *g, f* : *V* (*G*) → ℤ be functions such that *g*(*x*) *= f*(*x*) for all *x ∈ V* (*G*). If the set of edges of *G* can be decomposed into disjoint subsets
\(E(G) = {F_1}\cup{F_2}\cup\cdots\cup{F_n} \) so that every *Fi* induces a (*g, f*)-factor of *G*, then we say that *G* is (*g, f*)**- factorable**, and the above decomposition is called a (*g, f*)**-factorization** of *G*.We often regard an edge set *F* of a graph as its spanning subgraph with edge set *F*. As a special case of (*g, f*)-factorization, we can define **1-factorization**, *k***-regular factorization**, [a, b]**-factorization** and *f***-factorization**. In this chapter, we mainly investigate [a, b]-factorizations of graphs. We begin with some basic results on factorizations of special graphs.

## Keywords

Bipartite Graph Regular Graph Simple Graph Disjoint Subset General Graph## Preview

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