Collective Additive Tree Spanners of Bounded Tree-Breadth Graphs with Generalizations and Consequences
Feodor F. Dragan, Muad Abu-Ata

TL;DR
This paper explores how graphs with certain tree-decomposition properties admit small systems of collective additive or multiplicative tree spanners, providing polynomial algorithms to construct such systems with bounded stretch and size.
Contribution
It demonstrates converting multiplicative tree spanners into small sets of additive tree spanners and extends results to graphs with bounded tree-width, with polynomial-time algorithms.
Findings
Polynomial algorithms for constructing collective additive tree spanners.
Conversion of multiplicative to additive tree spanners with logarithmic size.
Extension to graphs with bounded tree-width and specific decomposition properties.
Abstract
In this paper, we study collective additive tree spanners for families of graphs enjoying special Robertson-Seymour's tree-decompositions, and demonstrate interesting consequences of obtained results. We say that a graph {\em admits a system of collective additive tree -spanners} (resp., {\em multiplicative tree -spanners}) if there is a system of at most spanning trees of such that for any two vertices of a spanning tree exists such that (resp., ). When one gets the notion of {\em additive tree -spanner} (resp., {\em multiplicative tree -spanner}). It is known that if a graph has a multiplicative tree -spanner, then admits a Robertson-Seymour's tree-decomposition with bags of radius at most in . We use this to demonstrate…
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Taxonomy
TopicsOptimization and Search Problems · Advanced Graph Theory Research · Nanocluster Synthesis and Applications
