### 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 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 polynomial-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.

Original language | English |
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Pages (from-to) | 441-465 |

Number of pages | 25 |

Journal | Journal of Graph Algorithms and Applications |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2015 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)
- Computer Science Applications
- Geometry and Topology
- Computational Theory and Mathematics

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## Cite this

*Journal of Graph Algorithms and Applications*,

*19*(1), 441-465. https://doi.org/10.7155/jgaa.00371