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  2. Tree (graph theory) - Wikipedia

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

    In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.

  3. Graph coloring - Wikipedia

    en.wikipedia.org/wiki/Graph_coloring

    An edge coloring with k colors is called a k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings. The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ ′ (G). A Tait coloring is a 3-edge coloring of a cubic graph.

  4. Spalting - Wikipedia

    en.wikipedia.org/wiki/Spalting

    Spalting is divided into three main types: pigmentation, white rot, and zone lines.Spalted wood may exhibit one or all of these types in varying degrees. Both hardwoods and softwoods can spalt, but zone lines and white rot are more commonly found on hardwoods due to enzymatic differences in white rotting fungi.

  5. Greedy coloring - Wikipedia

    en.wikipedia.org/wiki/Greedy_coloring

    In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...

  6. Brooks' theorem - Wikipedia

    en.wikipedia.org/wiki/Brooks'_theorem

    A greedy coloring starting from u and w and processing the remaining vertices of the spanning tree in bottom-up order, ending at v, uses at most Δ colors. For, when every vertex other than v is colored, it has an uncolored parent, so its already-colored neighbors cannot use up all the free colors, while at v the two neighbors u and w have ...

  7. Rainbow coloring - Wikipedia

    en.wikipedia.org/wiki/Rainbow_coloring

    An edge coloring of is called a -rainbow coloring if for every set of vertices of , there is a rainbow tree in containing the vertices of . The k {\displaystyle k} -rainbow index rx k ( G ) {\displaystyle {\text{rx}}_{k}(G)} of G {\displaystyle G} is the minimum number of colors needed in a k {\displaystyle k} -rainbow coloring of G ...

  8. Patterns in nature - Wikipedia

    en.wikipedia.org/wiki/Patterns_in_nature

    Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule purportedly satisfied by the cross-sectional areas of tree-branches. [4] [3] In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book ...

  9. Tracing garbage collection - Wikipedia

    en.wikipedia.org/wiki/Tracing_garbage_collection

    An example of tri-color marking on a heap with 8 objects. White, grey, and black objects are represented by light-grey, yellow, and blue, respectively. Because of these performance problems, most modern tracing garbage collectors implement some variant of the tri-color marking abstraction , but simple collectors (such as the mark-and-sweep ...

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