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Iterated arc graphs

Danny Rorabaugh, Claude Tardif, David Wehlau, Imed Zaguia (2018)

Commentationes Mathematicae Universitatis Carolinae

The arc graph δ ( G ) of a digraph G is the digraph with the set of arcs of G as vertex-set, where the arcs of δ ( G ) join consecutive arcs of G . In 1981, S. Poljak and V. Rödl characterized the chromatic number of δ ( G ) in terms of the chromatic number of G when G is symmetric (i.e., undirected). In contrast, directed graphs with equal chromatic numbers can have arc graphs with distinct chromatic numbers. Even though the arc graph of a symmetric graph is not symmetric, we show that the chromatic number of the...

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