Packing of spanning mixed arborescences

In this paper, we characterize a mixed graph F which contains k edge and arc-disjoint spanning mixed arborescences F 1 , horizontal ellipsis , F k, such that for each v is an element of V ( F ), the cardinality of { i is an element of [ k ] : v is the root of F i } lies in some prescribed interval. This generalizes both Nash-Williams and Tutte's theorem on spanning tree packing for undirected graphs and the previous characterization on digraphs which was given by Cai and Frank.

Automated summary

This paper generalizes the spanning tree packing theorem for undirected graphs by Nash-Williams and Tutte, while also extending the previous characterization on directed graphs by Cai and Frank.