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Unit and proper bitolerance digraphs
Author(s) -
Shull Randy,
Trenk Ann N.
Publication year - 1997
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199702)24:2<193::aid-jgt7>3.0.co;2-l
Subject(s) - digraph , combinatorics , mathematics , directed graph , class (philosophy) , discrete mathematics , graph , interval (graph theory) , computer science , artificial intelligence
In this paper we prove that the following statements about a directed graph G→ are equivalent. (1) G→ is a unit bitolerance digraph, (2) G→ is a proper bitolerance digraph, and (3) the digraph obtained by reversing all arc directions of G→ is an interval catch digraph (also known as a point‐core digraph). This result combined with known algorithms for recognizing interval catch digraphs, gives the first known polynomial‐time algorithm for recognizing a class of (bi)tolerance digraphs. © 1997 John Wiley & Sons, Inc.