Extending partial representations of function graphs and permutation graphs
Abstract
Function graphs are graphs representable by intersections of continuous real-valued functions on the interval [0,1] and are known to be exactly the complements of comparability graphs. As such they are recognizable in polynomial time. Function graphs generalize permutation graphs, which arise when all functions considered are linear. We focus on the problem of extending partial representations, which generalizes the recognition problem. We observe that for permutation graphs an easy extension of Golumbic's comparability graph recognition algorithm can be exploited. This approach fails for function graphs. Nevertheless, we present a polynomial-time algorithm for extending a partial representation of a graph by functions defined on the entire interval [0,1] provided for some of the vertices. On the other hand, we show that if a partial representation consists of functions defined on subintervals of [0,1], then the problem of extending this representation to functions on the entire interval [0,1] becomes NP-complete.
Cite
@article{arxiv.1204.6391,
title = {Extending partial representations of function graphs and permutation graphs},
author = {Pavel Klavík and Jan Kratochvíl and Tomasz Krawczyk and Bartosz Walczak},
journal= {arXiv preprint arXiv:1204.6391},
year = {2012}
}
Comments
Submitted to ESA 2012, track A