Simple reduction of f-colorings to edge-colorings

  • Xiao Zhou
  • Takao Nishizeki
Session 4A: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(v) times where f is a function assigning a natural number f(v) ∈ N to each vertex v ∈ V. In this paper we first give a simple reduction of the f-coloring problem to the ordinary edge-coloring problem, that is, we show that, given a graph G = (V, E) and a function f: V → N, one can directly construct in polynomial-time a new simple graph whose edge-coloring using a minimum number of colors immediately induces an f-coloring of G using a minimum number of colors. As by-products, we give a necessary and sufficient condition for a graph to have an f-factorization, and show that the edge-coloring problem for multigraphs can be easily reduced to edge-coloring problems for simple graphs.


Bipartite Graph Simple Graph Multiple Edge Factorization Problem Span Subgraph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Xiao Zhou
    • 1
  • Takao Nishizeki
    • 2
  1. 1.Education Center for Information PorcessingJapan
  2. 2.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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