Acyclically 3-colorable planar graphs

Patrizio Angelini () and Fabrizio Frati ()
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Patrizio Angelini: Università Roma Tre
Fabrizio Frati: Università Roma Tre

Journal of Combinatorial Optimization, 2012, vol. 24, issue 2, No 4, 116-130

Abstract: Abstract In this paper we study the acyclic 3-colorability of some subclasses of planar graphs. First, we show that there exist infinite classes of cubic planar graphs that are not acyclically 3-colorable. Then, we show that every planar graph has a subdivision with one vertex per edge that is acyclically 3-colorable and provide a linear-time coloring algorithm. Finally, we characterize the series-parallel graphs for which every 3-coloring is acyclic and provide a linear-time recognition algorithm for such graphs.

Keywords: Planar graphs; Acyclic coloring; Cubic graphs; Triconnectivity (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-011-9385-3

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