We present a new subclass of interval graphs that generalizes connected proper interval
graphs. These graphs are characterized by vertex orderings called connected perfect …

Vertex and edge orderings of graphs are commonly used in algorithmic graph theory. Such
orderings can encode structural properties of graphs in a condensed way and, thus, they …

When solving the Hamiltonian path problem it seems natural to be given additional
precedence constraints for the order in which the vertices are visited. For example one could …

Covering problems belong to the foundation of graph theory. There are several types of
covering problems in graph theory such as covering the vertex set by stars (domination …

Given disjoint source and sink sets, S={s_1, ..., s_k\} S= s 1,…, sk and T={t_1, ..., t_k\} T= t
1,…, tk, in a graph G, an unpaired k-disjoint path cover joining S and T is a set of pairwise …

The longest cycle problem is the problem of finding a cycle with maximal vertices in a graph.
Although it is solvable in polynomial time on few trivial graph classes, the longest cycle …

Let G be a connected interval graph with n vertices and m edges. For any positive integer k
and any subset S of E (G), we design an O (k| S|+ m) time algorithm to find a minimum k …

Given a graph G=(V, E) G=(V, E), A ⊆ VA⊆ V, and integers k and ℓ ℓ, the (A, ℓ)(A, ℓ)-Path
Packing problem asks to find k vertex-disjoint paths of length exactly ℓ ℓ that have endpoints …

A disjoint path cover of a graph is a set of internally vertex-disjoint paths that altogether
cover every vertex of the graph. Given two disjoint source and sink sets, S and T, in a graph …

Let G be some simple graph and k be any positive integer. Take h: V (G)→{0, 1,…, k+ 1} and
v∈ V (G), let AN h (v) denote the set of vertices w∈ NG (v) with h (w)≥ 1. Let AN h [v]= AN h …