2018/02/27 by Jeremy Kun, Michael P. O’Brien, Kun, Jeremy +5 · 1 citation
Computer Science · Engineering · #Advanced Graph Theory Research #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1802.09665
openalex publication_date 2018/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Low-treedepth colorings are an important tool for algorithms that exploit structure in classes of bounded expansion; they guarantee subgraphs that use few colors have bounded treedepth. These colorings have an implicit tradeoff between the total number of colors used and the treedepth bound, and prior empirical work suggests that the former dominates the run time of existing algorithms in practice. We introduce p-linear colorings as an alternative to the commonly used p-centered colorings. They can be efficiently computed in bounded expansion classes and use at most as many colors as p-centered colorings. Although a set of k