1 research outputs found
Completion of the mixed unit interval graphs hierarchy
We describe the missing class of the hierarchy of mixed unit interval graphs,
generated by the intersection graphs of closed, open and one type of half-open
intervals of the real line. 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 mention that the work in arXiv:1405.4247 directly extends to provide a
quadratic-time algorithm to recognize the class of mixed unit interval graphs.Comment: 17 pages, 36 figures (three not numbered). v1 Accepted in the TAMC
2015 conference. The recognition algorithm is faster in v2. One graph was not
listed in Theorem 7 of v1 of this paper v3 provides a proposition to
recognize the mixed unit interval graphs in quadratic time. v4 is a lot
cleare