2012/04/28 by Pavel Klavík, Jan Kratochvíl, Klavík, Pavel +6
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Constraint Satisfaction and Optimization #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph Theory and Algorithms #cs.DM #cs.DS #math.CO
paper · pdf · doi:10.48550/arxiv.1204.6391
Submitted to ESA 2012, track A
arxiv created 2012/04/28 · openalex publication_date 2012/04/28 · arxiv updated 2012/05/01 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
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.