A graph is probe (unit) interval if its vertices can be partitioned into two sets: a set of probe vertices and a set of nonprobe vertices, so that the set of nonprobe vertices is a stable set and it is possible to obtain ...

We study those unit interval graphs having a model with intervals of integer endpoints and prescribed length. We present a structural result for this graph subclass which leads to a quadratic-time recognition algorithm, ...

We study those unit interval graphs having a model with intervals of integer endpoints and prescribed length. We present a structural result for this graph subclass which leads to a quadratic-time recognition algorithm, ...

We present formulas to compute the P3 -interval number, the P3 -hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition, we find a connection between the ...

We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a ...

A Helly circular-arc model M=(C,A) is a circle C together with a Helly family A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a ...

This is the second and last chapter of a work in which we consider the unrestricted, minimal, and bounded representation problems for unit interval (UIG) and unit circular-arc (UCA) graphs. In the unrestricted version ...

This is the first of two chapters of a work in which we consider the unrestricted, minimal, and bounded representation problems for unit interval (UIG) and unit circular-arc (UCA) graphs. In the unrestricted version, a ...