2016/07/29 by Arie M. C. A. Koster, Koster, Arie, Robert Schweidweiler +3
Computer Science · Decision Sciences · #Advanced Graph Theory Research #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Scheduling and Timetabling Solutions
paper · pdf · doi:10.48550/arxiv.1607.08754
openalex publication_date 2016/07/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
An equitable graph coloring is a proper vertex coloring of a graph G where\nthe sizes of the color classes differ by at most one. The equitable chromatic\nnumber is the smallest number k such that G admits such equitable k-coloring.\nWe focus on enumerative algorithms for the computation of the equitable\ncoloring number and propose a general scheme to derive pruning rules for them:\nWe show how the extendability of a partial coloring into an equitable coloring\ncan be modeled via network flows. Thus, we obtain pruning rules which can be\nchecked via flow algorithms. Computational experiments show that the search\ntree of enumerative algorithms can be significantly reduced in size by these\nrules and, in most instances, such naive approach even yields a faster\nalgorithm. Moreover, the stability, i.e., the number of solved instances within\na given time limit, is greatly improved.\n Since the execution of flow algorithms at each node of a search tree is time\nconsuming, we derive arithmetic pruning rules (generalized Hall-conditions)\nfrom the network model. Adding these rules to an enumerative algorithm yields\nan even larger runtime improvement.\n