Reducing prime graphs and recognizing circle graphs

Abstract

We prove a reduction theorem for prime (simple) graphs in Cunningham’s sense. Roughly speaking this theorem says that every prime (simple) graph of ordern>5 “contains” a smaller prime graph of ordern−1. As an application we give a polynomial algorithm for recognizing circle graphs.

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Bouchet, A. Reducing prime graphs and recognizing circle graphs. Combinatorica 7, 243–254 (1987). https://doi.org/10.1007/BF02579301

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Keywords

  • Complete Bipartite Graph
  • Prime Graph
  • Canonical Decomposition
  • Circle Graph
  • Isotropic System