On Unique Independence Weighted Graphs
Computational Complexity
2009-07-02 v1 Discrete Mathematics
Abstract
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence vertex-weighted graph if it has a unique independent set with maximum sum of weights. Although, in this paper we observe that the problem of recognizing unique independence vertex-weighted graphs is NP-hard in general and therefore no efficient characterization can be expected in general; we give, however, some combinatorial characterizations of unique independence vertex-weighted graphs. This paper introduces a motivating application of this problem in the area of combinatorial auctions, as well.
Cite
@article{arxiv.0907.0088,
title = {On Unique Independence Weighted Graphs},
author = {Farzad Didehvar and Ali D. Mehrabi and Fatemeh Raee B},
journal= {arXiv preprint arXiv:0907.0088},
year = {2009}
}
Comments
9 pages, 1 figure