Completion of the mixed unit interval graphs hierarchy

On Restrictions of Balanced 2-Interval Graphs

The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify the introduction of a hierarchy of subclasses of 2-interval graphs that generalize line graphs: balanced 2-interval graphs, unit 2-interval graphs, and (x,x)...

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

Tenacity and some other Parameters of Interval Graphs can be computed in polynomial time

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...

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.

Tractability of parameterized completion problems on chordal and interval graphs: Minimum Fill-in and Physical Mapping

We study the parameterized complexity of several NP-Hard graph completion problems: The MINIMUM FILL-IN problem is to decide if a graph can be triangulated by adding at most k edges. We develop an O(k 5 mn + f(k)) algorithm for the problem on a graph with n vertices and m edges. In particular, this implies that the problem is xed parameter tractable (FPT). PROPER INTERVAL GRAPH COMPLETION probl...