In this work a matrix representation that characterizes the interval and proper interval graphs is presented, which is useful for the efficient formulation and solution of optimiz...
In this note, a constructive proof is given that the classes of proper interval graphs and unit interval graphs coincide, a result originally established by Fred S. Roberts. Addit...
In this paper we consider the k-fixed-endpoint path cover problem on proper interval graphs, which is a generalization of the path cover problem. Given a graph G and a set T of k v...
Given an arbitrary graph G = (V, E) and a proper interval graph H = (V, F) with E F we say that H is a proper interval completion of G. The graph H is called a minimal proper inte...
We present a linear time algorithm for the minimum linear arrangement problem on proper interval graphs. The obtained ordering is a 4-approximation for general interval graphs. 1 ...