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Tree-partitions of graphs with given pathwidth

· 2026 · math.CO · arXiv 2605.27780

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abstract

Graphs with bounded treewidth and bounded maximum degree are known to have tree-partitions of bounded width. What can be said if the bounded treewidth assumption is strengthened to bounded pathwidth? We prove that every graph with bounded pathwidth and bounded maximum degree has a tree-partition of bounded width, with the extra property that the underlying tree has bounded pathwidth. Moreover, we prove a lower bound showing that the bound on the pathwidth of the underlying tree is within a constant factor of optimal.

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math.CO 1

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2026 1

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Tree-partitions of graphs with bounded tree-depth

math.CO · 2026-08-13 · conditional · novelty 7.0

Every connected graph of tree-depth h admits a tree-partition of width at most max(1, (4h-10)Δ+1) whose indexing tree has radius at most h-1.

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  • Tree-partitions of graphs with bounded tree-depth math.CO · 2026-08-13 · conditional · none · ref 13 · internal anchor

    Every connected graph of tree-depth h admits a tree-partition of width at most max(1, (4h-10)Δ+1) whose indexing tree has radius at most h-1.