@techreport{7f458a7950d64aeba1b9238f31460133,
title = "Snakes and Ladders: a Treewidth Story",
abstract = " Let \$G\$ be an undirected graph. We say that \$G\$ contains a ladder of length \$k\$ if the \$2 \textbackslash{}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. ",
keywords = "math.CO, cs.DS, q-bio.PE",
author = "Steven Chaplick and Steven Kelk and Ruben Meuwese and Matus Mihalak and Georgios Stamoulis",
note = "12 pages plus 6 page appendix. 8 figures",
year = "2023",
month = feb,
day = "21",
language = "English",
type = "WorkingPaper",
}