General-demand disjoint path covers in a graph with faulty elements
نویسندگان
چکیده
A k-disjoint path cover of a graph is a set of k internally vertex-disjoint paths which cover the vertex set with k paths and each of which runs between a source and a sink. Given that each source and sink v is associated with an integer-valued demand d(v) ≥ 1, we are concerned with general-demand k-disjoint path cover in which every source and sink v is contained in the d(v) paths. In this paper, we present a reduction of a general-demand disjoint path cover problem to an unpaired many-to-many disjoint path cover problem, and obtain some results on disjoint path covers of restricted HL-graphs and proper interval graphs with faulty vertices and/or edges.
منابع مشابه
One-to-Many Disjoint Path Covers in a Graph with Faulty Elements
In a graph G, k disjoint paths joining a single source and k distinct sinks that cover all the vertices in the graph are called a one-tomany k-disjoint path cover of G. We consider a k-disjoint path cover in a graph with faulty vertices and/or edges obtained by merging two graphs H0 and H1, |V (H0)| = |V (H1)| = n, with n pairwise nonadjacent edges joining vertices in H0 and vertices in H1. We ...
متن کاملPaired Many-to-Many Disjoint Path Covers in Recursive Circulants and Tori
A paired many-to-many -disjoint path cover (paired -DPC) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants with ≥ and tori, and show that provided the number of faulty elements (vertices and/or edges) is or less, every nonbiparti...
متن کاملPaired many-to-many disjoint path covers in faulty hypercubes
A paired many-to-many k-disjoint path cover (k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all the vertices of the graph. Extending the notion of DPC, we define a paired many-to-many bipartite k-DPC of a bipartite graph G to be a set of k disjoint paths joining k distinct source-sink pairs that altogether cover the same number of vertic...
متن کاملMany-to-many Disjoint Path Covers in a Graph with Faulty Elements
In a graph G, k vertex disjoint paths joining k distinct sourcesink pairs that cover all the vertices in the graph are called a many-tomany k-disjoint path cover(k-DPC) of G. We consider an f -fault k-DPC problem that is concerned with finding many-to-many k-DPC in the presence of f or less faulty vertices and/or edges. We consider the graph obtained by merging two graphs H0 and H1, |V (H0)| = ...
متن کاملUnpaired Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks
An unpaired many-to-many -disjoint path cover (-DPC) of a graph is a set of disjoint paths joining distinct sources and sinks in which each vertex of is covered by a path. Here, a source can be freely matched to a sink. In this paper, we investigate unpaired many-to-many DPC's in a subclass of hpercube-like interconnection networks, called restricted HL-graphs, and show that every -d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Comput. Math.
دوره 89 شماره
صفحات -
تاریخ انتشار 2012