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Oriented Vertex and Arc Coloring of Edge Series-Parallel Digraphs

In: Operations Research Proceedings 2021

Author

Listed:
  • Frank Gurski

    (University of Düsseldorf)

  • Dominique Komander

    (University of Düsseldorf)

  • Marvin Lindemann

    (University of Düsseldorf)

Abstract

We study the oriented vertex and arc coloring problem on edge series-parallel digraphs which are related to the well known series-parallel graphs. The oriented class of edge series-parallel digraphs is recursively defined from pairs of vertices connected by a single arc and applying the parallel and series composition, which leads to specific orientations of undirected series-parallel graphs. We re-prove the known bound of 7 for the oriented chromatic number and the oriented chromatic index of series-parallel digraphs and we show that these bounds are tight even for edge series-parallel digraphs. Further, we give linear time solutions for computing the oriented chromatic number and the oriented chromatic index of minimal series-parallel digraphs and edge series-parallel digraphs.

Suggested Citation

  • Frank Gurski & Dominique Komander & Marvin Lindemann, 2022. "Oriented Vertex and Arc Coloring of Edge Series-Parallel Digraphs," Lecture Notes in Operations Research, in: Norbert Trautmann & Mario Gnägi (ed.), Operations Research Proceedings 2021, pages 101-106, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-08623-6_16
    DOI: 10.1007/978-3-031-08623-6_16
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