Author

Robert Hickingbotham

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Preprint Sep 2026

Induced Forest Minor Theorem for Graphs Without an Induced Star

Motivated by recent work on tree independence number, we study the path independence number of a graph $G$: the minimum integer $k$ such that there is a path decomposition of $G$ where each bag induces a graph with independence number at most $k$. We show that every graph excluding both an induced forest minor and an i...

Robert Hickingbotham, G. Joret · 1 citation

Jul 2026

Optimal tree-decompositions with bags of bounded pathwidth

We show that every planar graph has a tree-decomposition with optimal width such that the subgraph induced by each bag has pathwidth at most 3. This bound is best possible, and for tree-decompositions that satisfy a certain minimality condition, we in fact give a precise description of the possible structures in each b...

Kevin Hendrey, Robert Hickingbotham, Jędrzej Hodor et al. · arXiv.org · 0 citations