NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs
Computational Complexity
2012-01-18 v2
Abstract
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrary, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and M\"uller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with respect to the parameter "maximum degree".
Keywords
Cite
@article{arxiv.1110.1510,
title = {NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs},
author = {Sepp Hartung and André Nichterlein},
journal= {arXiv preprint arXiv:1110.1510},
year = {2012}
}
Comments
new author Sepp Hartung, new section with fixed-parameter tractability result; 25 pages, 4 figures