# Strong Edge-Coloring Of Planar Graphs

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 4, page 845-857
- ISSN: 2083-5892

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topWen-Yao Song, and Lian-Ying Miao. "Strong Edge-Coloring Of Planar Graphs." Discussiones Mathematicae Graph Theory 37.4 (2017): 845-857. <http://eudml.org/doc/288320>.

@article{Wen2017,

abstract = {A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known that every planar graph G has a strong edge-coloring with at most 4 Δ(G) + 4 colors [R.J. Faudree, A. Gyárfás, R.H. Schelp and Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211]. In this paper, we show that if G is a planar graph with g ≥ 5, then 𝜒's(G) ≤ 4(G) − 2 when Δ(G) ≥ 6 and 𝜒's(G) ≤ 19 when Δ(G) = 5, where g is the girth of G.},

author = {Wen-Yao Song, Lian-Ying Miao},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {strong edge-coloring; strong chromatic index; planar graph; dis- charging method.},

language = {eng},

number = {4},

pages = {845-857},

title = {Strong Edge-Coloring Of Planar Graphs},

url = {http://eudml.org/doc/288320},

volume = {37},

year = {2017},

}

TY - JOUR

AU - Wen-Yao Song

AU - Lian-Ying Miao

TI - Strong Edge-Coloring Of Planar Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 4

SP - 845

EP - 857

AB - A strong edge-coloring of a graph is a proper edge-coloring where each color class induces a matching. We denote by 𝜒's(G) the strong chromatic index of G which is the smallest integer k such that G can be strongly edge-colored with k colors. It is known that every planar graph G has a strong edge-coloring with at most 4 Δ(G) + 4 colors [R.J. Faudree, A. Gyárfás, R.H. Schelp and Zs. Tuza, The strong chromatic index of graphs, Ars Combin. 29B (1990) 205–211]. In this paper, we show that if G is a planar graph with g ≥ 5, then 𝜒's(G) ≤ 4(G) − 2 when Δ(G) ≥ 6 and 𝜒's(G) ≤ 19 when Δ(G) = 5, where g is the girth of G.

LA - eng

KW - strong edge-coloring; strong chromatic index; planar graph; dis- charging method.

UR - http://eudml.org/doc/288320

ER -

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