Incidence (graph)

In graph theory, an incidence is a pair $(u, e)$ where $u$ is a vertex and $e$ is an edge incident to $u$ .

Two distinct incidences $(u, e)$ and $(v,f)$ are adjacent if and only if $u = v$ , $e = f$ or $uv = e$ or $f$ .

An incidence coloring of a graph $G$ is an assignment of a color to each incidence of G in such a way that adjacent incidences get distinct colors. It is equivalent to a strong edge coloring of the graph obtained by subdivising once each edge of $G$ .

References

|The Incidence Coloring Page, by Éric Sopena.

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