Improved Approximation Algorithms for Path Vertex Covers in Regular Graphs

On Constrained Minimum Vertex Covers of Bipartite Graphs: Improved Algorithms

Path Algorithms on Regular Graphs

We consider standard algorithms of finite graph theory, like for instance shortest path algorithms. We present two general methods to polynomially extend these algorithms to infinite graphs generated by deterministic graph grammars.

Vertex Covers and Connected Vertex Covers in 3-connected Graphs

A vertex cover of a graph G=(V,E) is a subset N of V such that each element of E is incident upon some element of N, where V and E are the sets of vertices and of edges of G, respectively. A connected vertex cover of a graph G is a vertex cover of G such that the subgraph G[N] induced by N of G is connected. The minimum vertex cover problem (VCP) is the problem of finding a vertex cover of mini...

Algorithms for finding disjoint path covers in unit interval graphs

A many-to-many k-disjoint path cover (k-DPC for short) of a graph G joining the pairwise disjoint vertex sets S and T , each of size k, is a collection of k vertex-disjoint paths between S and T , which altogether cover every vertex of G. This is classified as paired, if each vertex of S must be joined to a specific vertex of T , or unpaired, if there is no such constraint. In this paper, we de...

Approximation Algorithms for Min-Max Capacitated Path Covers

This paper presents the first approximation algorithms and the first inapproximability results for minmax path cover problems, where a capacity constraint restricts the number of customers that can be serviced by every trip of the paths in the cover. Depending on different applications, every path in the cover may either be restricted to contain only one trip, or be allowed to contain multiple ...