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General results on tolerance intersection graphs
Author(s) -
Jacobson M. S.,
McMorris F. R.,
Scheinerman E. R.
Publication year - 1991
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/jgt.3190150603
Subject(s) - combinatorics , mathematics , indifference graph , chordal graph , intersection (aeronautics) , trapezoid graph , interval graph , intersection graph , discrete mathematics , pathwidth , interval (graph theory) , clique sum , block graph , 1 planar graph , graph , line graph , engineering , aerospace engineering
Abstract In this paper, general results are presented that are related to ϕ‐tolerance intersection graphs previously defined by Jacobson, McMorris, and Mulder. For example, it is shown that all graphs are ϕ‐tolerance intersection graphs for all ϕ, yet for “nice” ϕ, almost no graphs are ϕ‐tolerance interval graphs. Additional results about representation of trees are given.