On the Extension Theorem for Packing Steiner Forests
Jinghan A Zeng

TL;DR
This paper examines the conditions for packing edge-disjoint Steiner forests in graphs, identifies a flaw in Lau's proof, and provides corrected bounds for edge-connectivity needed to pack multiple Steiner forests.
Contribution
It identifies a gap in Lau's Extension Theorem and offers a corrected proof establishing new edge-connectivity bounds for packing Steiner forests.
Findings
Counterexample to Lau's Extension Theorem
Corrected proof with 36k edge-connectivity sufficiency
Refined bounds of 35k for k ≥ 8
Abstract
We consider the problem of packing edge-disjoint Steiner forests in a graph. The input consists of a multi-graph and a collection of vertex subsets . A Steiner forest for , also called an -forest, is a forest of in which each is connected. In the case where , this is the Steiner Tree packing problem. Kriesell's conjecture postulates that -edge-connectivity of is sufficient to find edge-disjoint -trees. Lau showed that -edge-connectivity suffices for the Steiner Tree packing problem, which was improved to by West and Wu and by Devos, McDonald and Pivotto. In his thesis, Lau asserts that for the Steiner Forest problem, if each is -edge-connected in , then there exist edge-disjoint -forests. However, Lau's proof relies on an intermediate theorem called the Extension…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Optimization and Packing Problems · Interconnection Networks and Systems
