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Acyclically 3-colorable planar graphs

Author

Listed:
  • Patrizio Angelini

    (Università Roma Tre)

  • Fabrizio Frati

    (Università Roma Tre)

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.

Suggested Citation

  • Patrizio Angelini & Fabrizio Frati, 2012. "Acyclically 3-colorable planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 116-130, August.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:2:d:10.1007_s10878-011-9385-3
    DOI: 10.1007/s10878-011-9385-3
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    Cited by:

    1. Huijuan Wang & Lidong Wu & Xin Zhang & Weili Wu & Bin Liu, 2016. "A note on the minimum number of choosability of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 31(3), pages 1013-1022, April.
    2. Huijuan Wang & Bin Liu & Xin Zhang & Lidong Wu & Weili Wu & Hongwei Gao, 2016. "List edge and list total coloring of planar graphs with maximum degree 8," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 188-197, July.
    3. Huijuan Wang & Lidong Wu & Weili Wu & Jianliang Wu, 2014. "Minimum number of disjoint linear forests covering a planar graph," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 274-287, July.
    4. Enqiang Zhu & Zepeng Li & Zehui Shao & Jin Xu & Chanjuan Liu, 2016. "Acyclic 3-coloring of generalized Petersen graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 902-911, February.

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