TY - GEN
T1 - Simple reduction of f-colorings to edge-colorings
AU - Zhou, Xiao
AU - Nishizeki, Takao
PY - 1995/1/1
Y1 - 1995/1/1
N2 - 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(υ) times where f is a function assigning a natural number f(υ) ∊ N to each vertex υ ∊ 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: υ → 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.
AB - 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(υ) times where f is a function assigning a natural number f(υ) ∊ N to each vertex υ ∊ 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: υ → 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.
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U2 - 10.1007/BFb0030836
DO - 10.1007/BFb0030836
M3 - Conference contribution
AN - SCOPUS:21844511060
SN - 354060216X
SN - 9783540602163
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 223
EP - 228
BT - Computing and Combinatorics - 1st Annual International Conference, COCOON 1995, Proceedings
A2 - Du, Ding-Zhu
A2 - Li, Ming
A2 - Du, Ding-Zhu
PB - Springer-Verlag
T2 - 1st Annual International Computing and Combinatorics Conference, COCOON 1995
Y2 - 24 August 1995 through 26 August 1995
ER -