Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval ...

Given an arbitrary graph and a proper interval graph with we say that H is a proper interval completion of G. The graph H is called a minimal proper interval completion of G if, for any sandwich graph with , is not a ...

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, ...

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 interval completion of G if, for any sandwich ...

We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to ...

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 interval completion of G if, for any sandwich ...

We develop a linear-space O(n+m) time algorithm to solve the cluster editing problem for proper interval models, where n and m are the number of vertices and edges of the represented graph.

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 interval completion of G if, for any sandwich ...