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[a, b]-Factorizations

  • Jin AkiyamaEmail author
  • Mikio Kano
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2031)

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Research Institute of Educational DevelopmentTokai UniversityTokyoJapan
  2. 2.Computer and Information SciencesIbaraki UniversityHitachiJapan

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