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A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular‐arc graphs, and nested interval graphs

1982/09/01 by Dale Skrien · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Combinatorics #Mathematics #Indifference graph #Interval graph #Pathwidth #Chordal graph #Split graph #Block graph #Cograph #Discrete mathematics #Comparability graph #Trapezoid graph #Maximal independent set #1-planar graph #Pancyclic graph #Graph #Line graph

paper · doi:10.1002/jgt.3190060307

openalex publication_date 1982/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Abstract Given a set F of digraphs, we say a graph G is a F ‐ graph (resp., F *‐ graph ) if it has an orientation (resp., acyclic orientation) that has no induced subdigraphs isomorphic to any of the digraphs in F . It is proved that all the classes of graphs mentioned in the title are F ‐graphs or F *‐graphs for subsets F of a set of three digraphs.

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