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Opposition graphs are strict quasi-parity graphs

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Abstract

An opposition graph is a graph whose edges can be acyclically oriented in such a way that every chordless path on four vertices has its extreme edges both pointing in or pointing out. A strict quasi-parity graph is a graphG such that every induced subgraphH ofG either is a clique or else contains a pair of vertices which are not endpoints of an odd (number of edges) chordless path ofH. The perfection of opposition graphs and strict quasi-parity graphs was established respectively by Olariu and Meyniel. We show here that opposition graphs are strict quasi-parity graphs.

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Authors and Affiliations

  1. Department of Computer Science, Rutgers University, 08903, NJ, USA

    C. T. Hoàng

  2. Rutgers Center for Operations Research, Rutgers University, 08903, NJ, USA

    F. Maffray

Authors
  1. C. T. Hoàng
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  2. F. Maffray
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Additional information

The second author acknowledges the support of the Air Force Office of Scientific Research under grant number AFOSR 0271 to Rutgers University.

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Hoàng, C.T., Maffray, F. Opposition graphs are strict quasi-parity graphs. Graphs and Combinatorics 5, 83–85 (1989). https://doi.org/10.1007/BF01788660

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  • DOI: https://doi.org/10.1007/BF01788660

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