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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)

Abstract

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.

Keywords

Bipartite Graph Simple Graph Multiple Edge Factorization Problem Span Subgraph 
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 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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