Linear Algorithm for Finding List Edge-Colorings of Series-Parallel Graphs

Tomoya FUJINO  Shuji ISOBE  Xiao ZHOU  Takao NISHIZEKI  

IEICE TRANSACTIONS on Information and Systems   Vol.E86-D   No.2   pp.186-190
Publication Date: 2003/02/01
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Selected Papers from LA Symposium)
Category: Graph Algorithms
algorithm,  list edge-coloring,  series-parallel graph,  

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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.