Bogdan AlecuVadim V. LozinQuiroz, DanielDanielQuirozRoman RabinovichIgor RazgonViktor Zamaraev2025-12-082025-12-082024-01-0110.1137/22m15240472-s2.0-85184851655https://cris-uv-2.scimago.es/handle/123456789/7962WOS:001171543400016Given two n-vertex graphs G1 and G2 of bounded treewidth, is there an n-vertex graph G of bounded treewidth having subgraphs isomorphic to G1 and G2? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if G1 is a binary tree and G2 is a ternary tree. We also provide an extensive study of cases where such ``gluing"" is possible. In particular, we prove that if G1 has treewidth k and G2 has pathwidth l, then there is an n-vertex graph of treewidth at most k + 3l + 1 containing both G1 and G2 as subgraphs.enacceso abiertoMathematics, AppliedMathematicsarticle