List Edge-Colorings of Series-Parallel Graphs

Tomoya FUJINO; Xiao ZHOU; Takao NISHIZEKI

List Edge-Colorings of Series-Parallel Graphs

Tomoya FUJINO, Xiao ZHOU, Takao NISHIZEKI

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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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if |L(e)| max{3,d(v),d(w)} for each edge e = vw, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.5 pp.1034-1045

Publication Date: 2003/05/01

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Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Tomoya FUJINO, Xiao ZHOU, Takao NISHIZEKI, "List Edge-Colorings of Series-Parallel Graphs" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 5, pp. 1034-1045, May 2003, doi: .
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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if |L(e)| max{3,d(v),d(w)} for each edge e = vw, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_5_1034/_p

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@ARTICLE{e86-a_5_1034,
author={Tomoya FUJINO, Xiao ZHOU, Takao NISHIZEKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={List Edge-Colorings of Series-Parallel Graphs},
year={2003},
volume={E86-A},
number={5},
pages={1034-1045},
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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if |L(e)| max{3,d(v),d(w)} for each edge e = vw, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - List Edge-Colorings of Series-Parallel Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1034
EP - 1045
AU - Tomoya FUJINO
AU - Xiao ZHOU
AU - Takao NISHIZEKI
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2003
AB - 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). In this paper, we prove that any series-parallel simple graph G has an L-edge-coloring if |L(e)| max{3,d(v),d(w)} for each edge e = vw, where d(v) and d(w) are the degrees of the ends v and w of e, respectively. Our proof yields a linear algorithm for finding an L-edge-coloring of series-parallel graphs.
ER -