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Completion of the mixed unit interval graphs hierarchy
Author(s) -
Talon Alexandre,
Kratochvíl Jan
Publication year - 2018
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.22159
Subject(s) - mathematics , unit interval , combinatorics , indifference graph , interval (graph theory) , class (philosophy) , intersection (aeronautics) , unit (ring theory) , chordal graph , interval graph , hierarchy , discrete mathematics , trapezoid graph , 1 planar graph , graph , computer science , mathematics education , artificial intelligence , economics , engineering , market economy , aerospace engineering
We describe the missing class of the hierarchy of mixed unit interval graphs. This class is generated by the intersection graphs of families of unit intervals that are allowed to be closed, open, and left‐closed‐right‐open. (By symmetry, considering closed, open, and right‐closed‐left‐open unit intervals generates the same class.) We show that this class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic‐time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also show that the algorithm from Shuchat et al. [8] directly extends to provide a quadratic‐time algorithm to recognize the class of mixed unit interval graphs.