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So far we have been mostly concerned with 'undirected' graphs ... can find a sequence of teams a,b,c,d,... where a beat b, and b beat c, and so on...
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Genus of a graph G. The smallest k such that G can be embedded on S(k) ... Let G be a connected graph that is 2-cell embedded on a surface of genus k. Then, ...
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Mathematical abstraction of the notion of a measurement ... eccentricity (of a vertex): e(v) = max {d(u,v) : u V} radius of G. rad(G) = min {e(v) : v V} ...
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The Art Gallery Problem. How many stationary guards are necessary ... Art Gallery. An art gallery will be represented by a polygon ... The Art Gallery Problem ...
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Many practical applications. Nodes: gates. Edges: wires between the gates ... If we can find a drawing of G where no edges cross, then we know that G is planar ...
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CSCI 4260-MATH 4150. Lecture 20. Approximation Algorithms for NP-Complete Problems ... This means that, in general, we can not solve these problems in polynomial time. ...
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To show equality, we need to present a coloring of K(5) that has no red or blue K3 ... v1 is adjacent to at most one red edge. Suppose (v1, v2), (v1, v3), (v1, ...
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