Linkages in Large Graphs of Bounded Tree-Width
Jan-Oliver Fr\"ohlich, Ken-ichi Kawarabayashi, Theodor M\"uller,, Julian Pott, Paul Wollan
TL;DR
The paper proves that large graphs with bounded tree-width and high connectivity are k-linked, supporting Thomassen's conjecture for graphs with slightly lower connectivity.
Contribution
It establishes that sufficiently large (2k+3)-connected graphs of bounded tree-width are k-linked, advancing understanding of graph connectivity and linkage properties.
Findings
Large (2k+3)-connected graphs of bounded tree-width are k-linked.
Supports Thomassen's conjecture for (2k+2)-connected graphs.
Provides conditions under which graphs are guaranteed to be k-linked.
Abstract
We show that all sufficiently large (2k+3)-connected graphs of bounded tree-width are k-linked. Thomassen has conjectured that all sufficiently large (2k+2)-connected graphs are k-linked.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Complexity and Algorithms in Graphs