2015/12/11 by Reinhard Diestel, Diestel, Reinhard
Computer Science · #05C05 #05C83 #06-XX #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Data Mining Algorithms and Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1512.03781
openalex publication_date 2015/12/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and matroids etc. Unlike graph-theoretical or order trees, these tree sets_ can provide a suitable formalization of tree structure also for infinite graphs, matroids, and set partitions. Order trees reappear as oriented tree sets. We show how each of the above structures defines a tree set, and which additional information, if any, is needed to reconstruct it from this tree set.