A note on the hardness of graph diameter augmentation problems
نویسندگان
چکیده
A graph has diameter D if every pair of vertices are connected by a path of at most D edges. The Diameter-D Augmentation problem asks how to add the a number of edges to a graph in order to make the resulting graph have diameter D. It was previously known that this problem is NP-hard [2], even in the D = 2 case. In this note, we give a simpler reduction to arrive at this fact and show that this problem is W[2]-hard.
منابع مشابه
A note on the order graph of a group
The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.
متن کاملA NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
متن کاملA note on hypergraph connectivity augmentation
We prove an abstract version of an edge-splitting theorem for directed hypergraphs that appeared in [1], and use this result to obtain min-max theorems on hypergraph augmentation problems that are linked to orientations. These problems include (k, l)-edge-connectivity augmentation of directed hypergraphs, and (k, l)-partition-connectivity augmentation of undirected hypergraphs by uniform hypere...
متن کاملA note on a graph related to the comaximal ideal graph of a commutative ring
The rings considered in this article are commutative with identity which admit at least two maximal ideals. This article is inspired by the work done on the comaximal ideal graph of a commutative ring. Let R be a ring. We associate an undirected graph to R denoted by mathcal{G}(R), whose vertex set is the set of all proper ideals I of R such that Inotsubseteq J(R), where J(R) is...
متن کاملEffect of friction stir welding parameters on the microstructure and mechanical properties of dissimilar AA2024-AA6061 joints
In the present study, to resolve the problems in fusion welding methods as well as to increase the strength, FSW method was used to join aluminum alloy sheets 6061 and 2024. Moreover, optimal parameters for joining of these two alloys were also taken into consideration. Various tool rotation speeds of 565, 950 and 1500 rpm were selected. For each tool rotation speed, two traverse speed variable...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/0909.3877 شماره
صفحات -
تاریخ انتشار 2009