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math.CO2025
Lassos: Pushing Tree Decompositions Forward Along Homomorphisms
Benjamin Merlin Bumpus, James Fairbanks, Will J. Turner
It is folklore that tree-width is monotone under taking subgraphs (i.e. injective graph homomorphisms) and contractions (certain kinds of surjective graph homomorphisms). However,…
math.CO2025
Directed branch-width: A directed analogue of tree-width
Benjamin Merlin Bumpus, Kitty Meeks, William Pettersson
Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking wheth…