Graph Orientations Optimizing the Number of Light or Heavy Vertices

Abstract

This paper introduces four graph orientation problems named Maximize W -Light, Minimize W -Light, Maximize W -Heavy, and Minimize W -Heavy, where W can be any fixed non-negative integer. In each of these problems, the input is an undirected graph G and the objective is to assign a direction to each edge in G so that the number of vertices with outdegree at most W or at least W in the resulting directed graph is maximized or minimized. We derive a number of results on the computational complexity and polynomial-time approximability of these problems for different values of W and various special classes of graphs. In particular, we show that Maximize 0-Light and Minimize 1-Heavy are equivalent to Maximum Independent Set and Minimum Vertex Cover, respectively, so by allowing the value of W to vary, we obtain a new, natural generalization of the two latter problems.KeywordsPlanar GraphUndirected GraphVertex CoverMaximum CliqueChordal GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.