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  2. Tree (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Tree_(graph_theory)

    A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v, then the label of u is smaller than the label of v). In a rooted tree, the parent of a vertex v is the vertex connected to v on the path to the root; every vertex has a unique parent, except the root has no parent. [24]

  3. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5] Monochromatic triangle [3]: GT6 Pathwidth, [6] or, equivalently, interval thickness, and vertex separation number [7] Rank coloring; k-Chinese postman

  4. Link/cut tree - Wikipedia

    en.wikipedia.org/wiki/Link/cut_tree

    In particular, we can adjust it to merge (link) and split (cut) in O(log(n)) amortized time. Link/cut trees divide each tree in the represented forest into vertex-disjoint paths, where each path is represented by an auxiliary data structure (often splay trees, though the original paper predates splay trees and thus uses biased binary search ...

  5. Tree decomposition - Wikipedia

    en.wikipedia.org/wiki/Tree_decomposition

    Thus, given a graph G = (V, E), a tree decomposition is a pair (X, T), where X = {X 1, …, X n} is a family of subsets (sometimes called bags) of V, and T is a tree whose nodes are the subsets X i, satisfying the following properties: [3] The union of all sets X i equals V. That is, each graph vertex is associated with at least one tree node.

  6. SPQR tree - Wikipedia

    en.wikipedia.org/wiki/SPQR_tree

    Label each split component with a P (a two-vertex split component with multiple edges), an S (a split component in the form of a triangle), or an R (any other split component). While there exist two split components that share a linked pair of virtual edges, and both components have type S or both have type P, merge them into a single larger ...

  7. Biconnected component - Wikipedia

    en.wikipedia.org/wiki/Biconnected_component

    A cutpoint, cut vertex, or articulation point of a graph G is a vertex that is shared by two or more blocks. The structure of the blocks and cutpoints of a connected graph can be described by a tree called the block-cut tree or BC-tree. This tree has a vertex for each block and for each articulation point of the given graph.

  8. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    Move over, Wordle, Connections and Mini Crossword—there's a new NYT word game in town! The New York Times' recent game, "Strands," is becoming more and more popular as another daily activity ...

  9. Spanning tree - Wikipedia

    en.wikipedia.org/wiki/Spanning_tree

    In either case, one can form a spanning tree by connecting each vertex, other than the root vertex v, to the vertex from which it was discovered. This tree is known as a depth-first search tree or a breadth-first search tree according to the graph exploration algorithm used to construct it. [ 18 ]