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[a, b]-Factorizations

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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Correspondence to Jin Akiyama .

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© 2011 Springer-Verlag Berlin Heidelberg

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Akiyama, J., Kano, M. (2011). [a, b]-Factorizations. In: Factors and Factorizations of Graphs. Lecture Notes in Mathematics(), vol 2031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21919-1_5

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