Packing spanning arborescences with extra large one
Hui Gao

TL;DR
This paper extends classical graph theorems on edge-disjoint spanning trees to directed graphs, providing new conditions for their existence and properties, inspired by fractional and structural graph theory concepts.
Contribution
It offers a digraphic version of Fang and Yang's extension of Nash-Williams and Tutte's theorem, advancing understanding of spanning structures in directed graphs.
Findings
Provides a digraphic analogue of Fang and Yang's theorem
Establishes new conditions for edge-disjoint spanning trees in directed graphs
Highlights open problems in mixed graphic versions
Abstract
The celebrated Nash-Williams and Tutte's theorem states that a graph contains edge disjoint spanning trees if and only if , where Inspired by the NDT theorem as structural explanations for the fractional part of Nash-Williams' forest decomposition theorem, Fang and Yang extended Nash-Williams and Tutte's theorem and proved that if , then contains edge disjoint spanning trees and another forest with , and if is not a spanning tree, then has a component with at least edges. In this paper, we give a digraphic version of their result; however, the mixed graphic version remains open.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Complexity and Algorithms in Graphs
