Mixed unit interval graphs

Unit Mixed Interval Graphs

In this paper we extend the work of Rautenbach and Szwarcfiter [8] by giving a structural characterization of graphs that can be represented by the intersection of unit intervals that may or may not contain their endpoints. A characterization was proved independently by Joos in [6], however our approach provides an algorithm that produces such a representation, as well as a forbidden graph char...

Integral Mixed Unit Interval Graphs

We characterize graphs that have intersection representations using unit intervals with open or closed ends such that all ends of the intervals are integral in terms of infinitely many minimal forbidden induced subgraphs. Furthermore, we provide a quadratic-time algorithm that decides if a given interval graph admits such an intersection representation.

M1 internship report: problems on interval graphs L(2,1)-labelling Almost-mixed unit interval graphs

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 cl...

Precoloring extension on unit interval graphs

In the precoloring extension problem we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [6], we show that the precoloring extension problem is NP-complete on unit interval graphs.