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math.CO2026
Co-Decompositions and FO Model Checking
Benjamin Merlin Bumpus, Guilherme C. M. Gomes, Laura Larios-Jones +1
Tree decompositions describe large graphs as gluings of smaller component parts. Here we study their categorical duals, tree co-decompositions, which construct large graphs via fib…
math.CO2024
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,…