### Abstract

Assume that each edge e of a graph G is assigned a list (set) L(e) of colors. Then an edge-coloring of G is called an L-edge-coloring if each edge e of G is colored with a color contained in L(e). It is known that any series-parallel simple graph G has an L-edge-coloring if either (i) |L(e)| ≥ max{4, d(v), d(w)} for each edge e = vw or (ii) the maximum degree of G is at most three and |L(e)| ≥ 3 for each edge e, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. In this paper we give a linear-time algorithm for finding such an L-edge-coloring of a series-parallel graph G.

Original language | English |
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Pages (from-to) | 186-190 |

Number of pages | 5 |

Journal | IEICE Transactions on Information and Systems |

Volume | E86-D |

Issue number | 2 |

Publication status | Published - 2003 Feb |

### Keywords

- Algorithm
- List edge-coloring
- Series-parallel graph

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

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## Cite this

Fujino, T., Isobe, S., Zhou, X., & Nishizeki, T. (2003). Linear algorithm for finding list edge-colorings of series-parallel graphs.

*IEICE Transactions on Information and Systems*,*E86-D*(2), 186-190.