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The sum of the labels is 11, smaller than could be achieved using only two labels. In graph theory, a sum coloring of a graph is a labeling of its vertices by positive integers, with no two adjacent vertices having equal labels, that minimizes the sum of the labels. The minimum sum that can be achieved is called the chromatic sum of the graph. [1]
The criterion of minimalization is the sum of colors Star coloring Every 2-chromatic subgraph is a disjoint collection of stars Strong coloring Every color appears in every partition of equal size exactly once Strong edge coloring Edges are colored such that each color class induces a matching (equivalent to coloring the square of the line graph)
The American Society of Cinematographers (ASC) defines lighting ratio as (key+fill):fill, or (key+Σ fill):Σ fill, where Σ fill is the sum of all fill lights. Light can be measured in footcandles. A key light of 200 footcandles and fill light of 100 footcandles have a 3:1 ratio (a ratio of three to one) — (200 + 100):100.
We can also generalize the induced Ramsey's theorem to a multicolor setting. For graphs H 1, H 2, …, H r, define r ind (H 1, H 2, …, H r) to be the minimum number of vertices in a graph G such that any coloring of the edges of G into r colors contain an induced subgraph isomorphic to H i where all edges are colored in the i-th color for ...
This would have established the four color theorem. No graph can be 0-colored, so 0 is always a chromatic root. Only edgeless graphs can be 1-colored, so 1 is a chromatic root of every graph with at least one edge. On the other hand, except for these two points, no graph can have a chromatic root at a real number smaller than or equal to 32/27. [8]
When one of the components has the strongest intensity, the color is a hue near this primary color (red-ish, green-ish, or blue-ish), and when two components have the same strongest intensity, then the color is a hue of a secondary color (a shade of cyan, magenta, or yellow). A secondary color is formed by the sum of two primary colors of equal ...
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The complete bipartite graph K 3,3 with each of its color classes drawn as parallel line segments on distinct lines. Folkman & Fulkerson (1969) investigated the non-increasing sequences of numbers m 1, m 2, m 3, ... with the property that there exists a proper edge coloring of a given graph G with m 1 edges of the first color, m 2 edges of the ...