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In graph theory, a partial k-tree is a type of graph, defined either as a subgraph of a k-tree or as a graph with treewidth at most k. [1] Many NP-hard combinatorial problems on graphs are solvable in polynomial time when restricted to the partial k -trees, for bounded values of k .
The Goldner–Harary graph, an example of a planar 3-tree.. In graph theory, a k-tree is an undirected graph formed by starting with a (k + 1)-vertex complete graph and then repeatedly adding vertices in such a way that each added vertex v has exactly k neighbors U such that, together, the k + 1 vertices formed by v and U form a clique.
A BK-tree is a metric tree suggested by Walter Austin Burkhard and Robert M. Keller specifically adapted to discrete metric spaces.For simplicity, consider integer discrete metric (,).
An arrangement of nine points (related to the Pappus configuration) forming ten 3-point lines.. In discrete geometry, the original orchard-planting problem (or the tree-planting problem) asks for the maximum number of 3-point lines attainable by a configuration of a specific number of points in the plane.
The leaves are arranged alternately along the twigs and are broadly oblong or ovate, 10–12 centimetres (4– 4 + 1 ⁄ 2 in) long by 7–8 cm (2 + 3 ⁄ 4 – 3 + 1 ⁄ 4 in) wide, with a short (typically 2–3 millimetres or 1 ⁄ 16 – 1 ⁄ 8 inch) petiole. They have a cordate (auricled) base and 3–6 rounded lobes, divided no further ...
The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
The sessile oak is a large deciduous tree up to 40 metres (130 feet) tall, [10] in the white oak section of the genus (Quercus sect. Quercus) and similar to the pedunculate oak (Q. robur), with which it overlaps extensively in range.
Young female cone Pinus sylvestris forest in Sierra de Guadarrama, central Spain. Pinus sylvestris is an evergreen coniferous tree growing up to 35 metres (115 feet) in height [4] and 1 m (3 ft 3 in) in trunk diameter when mature, [5] exceptionally over 45 m (148 ft) tall and 1.7 m (5 + 1 ⁄ 2 ft) in trunk diameter on very productive sites.