The longest path problem is the problem of finding a path of maximum length in a graph.
Polynomial solutions for this problem are known only for small classes of graphs, while it is …

Given a graph G, the longest path problem asks to compute a simple path of G with the
largest number of vertices. This problem is the most natural optimization version of the well …

While the theory of labelled well-quasi-order has received significant attention in the graph
setting, it has not yet been considered in the context of permutation patterns. We initiate this …

Abstract An L (2, 1)-labeling of a graph is an assignment of non-negative integers, called
colours to the vertex set of G such that the difference between the colours assigned to …

Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its
internal vertices have distinct colors. We say that the graph is rainbow vertex-connected if …

We prove two dichotomy results for detecting long paths as patterns in a given graph. The
NP-hard problem Longest Induced Path is to determine the longest induced path in a graph …

The critical path problem, in Software Project Management, finds the longest path in a
Directed Acyclic Graph. The problem is immensely important for scheduling the critical …

The longest path problem is the problem of finding a path of maximum length in a graph. As
a generalization of the Hamiltonian path problem, it is NP-complete on general graphs and …

Let G be a connected graph. The eccentricity of a path P, denoted by ecc G (P), is the
maximum distance from P to any vertex in G. In the Central path (CP) problem, our aim is to …

The longest path problem is the problem of finding a path of maximum length in a graph.
Polynomial solutions for this problem are known only for small classes of graphs, while it is …