منابع مشابه
Identifying path covers in graphs
This paper introduces the problem of identifying vertices of a graph using paths. An identifying path cover of a graph G is a set P of paths such that each vertex belongs to a path of P, and for each pair u, v of vertices, there is a path of P which includes exactly one of u, v. This new notion is related to a large number of other identi cation problems in graphs and hypergraphs. We study the ...
متن کاملIdentifying Vertex Covers in Graphs
An identifying vertex cover in a graph G is a subset T of vertices in G that has a nonempty intersection with every edge of G such that T distinguishes the edges, that is, e∩T 6= ∅ for every edge e in G and e∩T 6= f ∩T for every two distinct edges e and f in G. The identifying vertex cover number τD(G) of G is the minimum size of an identifying vertex cover in G. We observe that τD(G) + ρ(G) = ...
متن کاملSimple Path Covers in Graphs
A simple path cover of a graph G is a collection ψ of paths in G such that every edge of G is in exactly one path in ψ and any two paths in ψ have at most one vertex in common. More generally, for any integer k ≥ 1, a Smarandache path k-cover of a graph G is a collection ψ of paths in G such that each edge of G is in at least one path of ψ and two paths of ψ have at most k vertices in common. T...
متن کاملAlgorithms 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...
متن کاملDisjoint path covers in cubes of connected graphs
Given a graph G, and two vertex sets S and T of size k each, a many-tomany k-disjoint path cover of G joining S and T is a collection of k disjoint paths between S and T that cover every vertex of G. It is classified as paired if each vertex of S must be joined to a designated vertex of T , or unpaired if there is no such constraint. In this article, we first present a necessary and sufficient ...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2013
ISSN: 1570-8667
DOI: 10.1016/j.jda.2013.07.006