Abstract

Let $G$ be an undirected graph. We say that $G$ contains a ladder of length $k$ if the $2 \times (k+1)$ grid graph is an induced subgraph of $G$ that is only connected to the rest of $G$ via its four cornerpoints. We prove that if all the ladders contained in $G$ are reduced to length 4, the treewidth remains unchanged (and that this bound is tight). Our result indicates that, when computing the treewidth of a graph, long ladders can simply be reduced, and that minimal forbidden minors for bounded treewidth graphs cannot contain long ladders. Our result also settles an open problem from algorithmic phylogenetics: the common chain reduction rule, used to simplify the comparison of two evolutionary trees, is treewidth-preserving in the display graph of the two trees.
Original languageEnglish
Publication statusPublished - 21 Feb 2023

Keywords

  • math.CO
  • cs.DS
  • q-bio.PE

Fingerprint

Dive into the research topics of 'Snakes and Ladders: a Treewidth Story'. Together they form a unique fingerprint.
  • Snakes and Ladders: A Treewidth Story

    Chaplick, S., Kelk, S., Meuwese, R., Mihalák, M. & Stamoulis, G., 2023, Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers: 49th International Workshop, WG 2023, Fribourg, Switzerland, June 28–30, 2023, Revised Selected Papers. Paulusma, D. & Ries, B. (eds.). Springer, Cham, p. 187-200 14 p. (Lecture Notes in Computer Science, Vol. 14093).

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Cite this