Graph theory is afundamental branch of mathematicsthat studiesnetworksconsisting of
nodes (vertices) and their connections (edges). Extensive research has been conducted on …

When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …

We present a simple linear time algorithm for unit interval graph recognition. This algorithm
uses 3 LBFS sweeps and then a very simple test to determine if the given graph is a unit …

We prove that the complements of interval bigraphs are precisely those circular arc graphs
of clique covering number two, which admit a representation without two arcs covering the …

In this note, a constructive proof that the classes of proper interval graphs and unit interval
graphs coincide is given, a result originally established by Fred S. Roberts. Additionally, the …

In this paper we study the problem of recognizing and representing dynamically changing
proper interval graphs. The input to the problem consists of a series of modifications to be …

We propose a linear time recognition algorithm for proper interval graphs. The algorithm is
based on certain ordering of vertices, called bicompatible elimination ordering (BCO). Given …

Recently, D. Corneil found a simple 3-sweep lexicographic breadth first search (LexBFS)
algorithm for the recognition of proper interval graphs. We point out how to modify Corneil's …

Chordal graphs are intersection graphs of subtrees of a tree T. We investigate the complexity
of the partial representation extension problem for chordal graphs. A partial representation …

Signed graphs, ie, undirected graphs with edges labelled with a plus or minus sign, are
commonly used to model relationships in social networks. Recently, Kermarrec and Thraves …