Graph Orientations Optimizing the Number of Light or Heavy Vertices

Yuichi Asahiro, Jesper Jansson, Eiji Miyano, Hirotaka Ono
2015 Journal of Graph Algorithms and Applications  
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 problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every 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. A number of results on the computational complexity and
more » ... lynomial-time approximability of these problems for different values of W and various special classes of graphs are derived. In particular, it is shown that Maximize 0-Light and Minimize 1-Heavy are identical to Maximum Independent Set and Minimum Vertex Cover, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.
doi:10.7155/jgaa.00371 fatcat:2qcxqbkia5holly22b3a5k3iri