# Strong edge coloring sparse graphs

2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A strong edge coloring of a graph is a proper edge coloring such that no edge has two incident edges of the same color. Erdős and Nešetřil conjectured in 1989 that $5 /4∆2$ colors are always enough for a strong edge coloring, where $∆$ is the maximum degree of the graph. In the specific case where $∆ = 4$, we prove this to be true when there is no subgraph with average degree at least $4 − 1/5$ , and show that fewer colors are necessary when the graph is even sparser.
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Cited literature [11 references]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01264420
Contributor : Alexandre Pinlou <>
Submitted on : Wednesday, July 27, 2016 - 10:25:02 AM
Last modification on : Thursday, April 9, 2020 - 10:58:11 AM

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### Citation

Julien Bensmail, Marthe Bonamy, Hervé Hocquard. Strong edge coloring sparse graphs. Electronic Notes in Discrete Mathematics, Elsevier, 2015, The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015, 49, pp.773-778. ⟨10.1016/j.endm.2015.06.104⟩. ⟨lirmm-01264420⟩

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