Geodesic
On the maximum average degree and the incidence chromatic number of a graph
Discrete mathematics & theoretical computer science, Tome 7 (2005).

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We prove that the incidence chromatic number of every 3-degenerated graph G is at most Δ (G)+4. It is known that the incidence chromatic number of every graph G with maximum average degree mad(G)<3 is at most Δ (G)+3. We show that when Δ (G) ≥ 5, this bound may be decreased to Δ (G)+2. Moreover, we show that for every graph G with mad(G)<22/9 (resp. with mad(G)<16/7 and Δ (G)≥ 4), this bound may be decreased to Δ (G)+2 (resp. to Δ (G)+1). 
@article{DMTCS_2005_7_a7,
     author = {Dolama, Mohammad Hosseini and Sopena, Eric},
     title = {On the maximum average degree and the incidence chromatic number of a graph},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {7},
     year = {2005},
     doi = {10.46298/dmtcs.349},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.349/}
}
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Dolama, Mohammad Hosseini; Sopena, Eric. On the maximum average degree and the incidence chromatic number of a graph. Discrete mathematics & theoretical computer science, Tome 7 (2005). doi : 10.46298/dmtcs.349. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.349/

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