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Above:A 3:1-coloring of the cycle on 5 vertices, and the corresponding 6:2-coloring. Below: A 5:2 coloring of the same graph. A b-fold coloring of a graph G is an assignment of sets of size b to vertices of a graph such that adjacent vertices receive disjoint sets. An a:b-coloring is a b-fold coloring out of a available colors.
Given a graph G = (V, E), a fractional matching in G is a function that assigns, to each edge e in E, a fraction f(e) in [0, 1], such that for every vertex v in V, the sum of fractions of edges adjacent to v is at most 1: [1]: A matching in the traditional sense is a special case of a fractional matching, in which the fraction of every edge is either 0 or 1: f(e) = 1 if e is in the matching ...
Painters refer to this as "adding black". In our illustration, one projector is set to full intensity, a second is set to some intensity between zero and full, and third is set to zero. "Dimming" is accomplished by decreasing each projector's intensity setting to the same fraction of its start setting.
An interval incidence coloring of G is an incidence coloring c such that for each vertex v of G the set () is an interval. [11] [12] The interval incidence coloring number of G is the minimum number of colors used for the interval incidence coloring of G. It is denoted by .
A Washington, D.C. man has been arrested for threatening flight attendants on a United Airlines plane traveling from Houston to New Jersey. Kedus Yacob Damtew, 38, was charged with one count of ...
Move over, hot chocolate and egg nog — it seems steamed-up Dr Pepper is the new cold weather beverage of choice. In a video posted on Instagram, user Morgan Chomps kickstarted a new trend: Dr ...