A simple graph G is k-ordered (respectively, k-ordered hamiltonian), if for any sequence of k distinct vertices v1, . . . , vk of G there exists a cycle (respectively, hamiltonian...
This paper focuses on first-order logic (FO) extended by reachability predicates such that the expressiveness and hence decidability properties lie between FO and monadic second-o...
Robertson and Seymour (1990) proved that graphs of bounded tree-width are well-quasi-ordered by the graph minor relation. By extending their arguments, Geelen, Gerards, and Whittle...