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An incidence coloring of $G$ is a coloring of its incidences assigning distinct colors to adjacent incidences. It was conjectured that at most $\\Delta(G) + 2$ colors are needed for an incidence coloring of any graph $G$. The conjecture is false in general, but the bound holds for many classes of graphs. 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Two incidences $(v,e)$ and $(u,f)$ are adjacent if at least one of the following holds: $(a)$ $v = u$, $(b)$ $e = f$, or $(c)$ $vu \\in \\{e,f\\}$. An incidence coloring of $G$ is a coloring of its incidences assigning distinct colors to adjacent incidences. It was conjectured that at most $\\Delta(G) + 2$ colors are needed for an incidence coloring of any graph $G$. The conjecture is false in general, but the bound holds for many classes of graphs. 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