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For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 / 2 ≡ 2 (mod 3). Equivalently, 2 n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 2 (mod 3) . Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).
In graph theory, total coloring is a type of graph coloring on the vertices and edges of a graph. When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent edges, no adjacent vertices and no edge and either endvertex are assigned the same color. The total chromatic number χ″ ( G) of a ...
Weak 2-coloring. In graph theory, a weak coloring is a special case of a graph labeling. A weak k -coloring of a graph G = (V, E) assigns a color c(v) ∈ {1, 2, ..., k } to each vertex v ∈ V, such that each non- isolated vertex is adjacent to at least one vertex with different color. In notation, for each non-isolated v ∈ V, there is a ...
Cache coloring. In computer science, cache coloring (also known as page coloring) is the process of attempting to allocate free pages that are contiguous from the CPU cache 's point of view, in order to maximize the total number of pages cached by the processor. Cache coloring is typically employed by low-level dynamic memory allocation code in ...
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ISBN. 978-0486256641. LC Class. Q162.G23. One Two Three... Infinity: Facts and Speculations of Science is a popular science book by theoretical physicist George Gamow, first published in 1947, but still (as of 2020) available in print and electronic formats. The book explores a wide range of fundamental concepts in mathematics and science ...
List coloring. In graph theory, a branch of mathematics, list coloring is a type of graph coloring where each vertex can be restricted to a list of allowed colors. It was first studied in the 1970s in independent papers by Vizing and by Erdős, Rubin, and Taylor. [1]
A covering system is called irredundant (or minimal) if all the residue classes are required to cover the integers. The first two examples are disjoint. The third example is distinct. A system (i.e., an unordered multi-set) of finitely many residue classes is called an -cover if it covers every integer at least times, and an exact -cover if it ...
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