Containment Graphs and Posets of Paths in a Tree: Wheels and Partial Wheels

Martin Charles Golumbic, Vincent Limouzy

Research output: Contribution to journalArticlepeer-review


We consider questions regarding the containment graphs of paths in a tree (CPT graphs), a subclass of comparability graphs, and the containment posets of paths in a tree (CPT orders). In 1984, Corneil and Golumbic observed that a graph G may be CPT, yet not every transitive orientation of G necessarily has a CPT representation, illustrating this on the even wheels W2k(k ≥ 3). Motivated by this example, we characterize the partial wheels that are containment graphs of paths in a tree, and give a number of examples and obstructions for this class. Our characterization gives the surprising result that all partial wheels that admit a transitive orientation are CPT graphs. We then characterize the CPT orders whose comparability graph is a partial wheel.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
Issue number1
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature B.V.


  • CPT order
  • Containment graph
  • Containment order
  • Containment poset
  • Partial wheel
  • Paths in a tree
  • Transitive orientation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics


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