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Orientations without forbidden patterns on three vertices

Author

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  • Guzmán-Pro, Santiago
  • Hernández-Cruz, César

Abstract

Given a set F of oriented graphs, a graph G is a Forbe(F)-graph if it admits an F-free orientation. Skrien showed that proper-circular arc graphs, nested interval graphs and comparability graphs, correspond to Forbe(F)-graph classes for some set F of orientations of P3. Building on these results, we exhibit the list of all Forbe(F)-graph classes when F is a set of oriented graphs on three vertices. Structural characterizations for these classes are provided, except for the so-called perfectly-orientable graphs and the transitive-perfectly-orientable graphs, which remain as open problems.

Suggested Citation

  • Guzmán-Pro, Santiago & Hernández-Cruz, César, 2024. "Orientations without forbidden patterns on three vertices," Applied Mathematics and Computation, Elsevier, vol. 480(C).
    • Handle: RePEc:eee:apmaco:v:480:y:2024:i:c:s0096300324003734
    DOI: 10.1016/j.amc.2024.128912
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