A data structure of this type uses an associative array on integer keys to point to substructures with square root of n elements, which helps that type of these structures achieve log log n running times for search and deletion; that type of these structures is named for (*) van Emde Boas.
Given a well-quasi-ordered preorder on sigma, the preorder on these structures of a homeomorphic embedding of sigma is well-quasi-ordered according to Kruskal's theorem about these structures. A data structure of this type uses an associative array on integer keys to point to substructures with square root of n elements, which helps that type of these structures achieve log log n running times for search and deletion; that type of these structures is named for (*) van Emde Boas. Rotations are used to maintain the invariants of a data structure of this type that is usually implemented as "left-leaning" and colors nodes. A recursive definition usually consists of either a value or more of these structures. A connected graph with no cycles is one of these structures. For 10 points, name these structures that come in B and red-black types, groups of which are called forests.
Given a well-quasi-ordered preorder on sigma, the preorder on these structures of a homeomorphic embedding of sigma is well-quasi-ordered according to Kruskal's theorem about these structures.
trees [prompt on “graphs”]