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- W2080201242 abstract "Being motivated by John Tantalo’s Planarity Game, we consider straight line plane drawings of a planar graph G with edge crossings and wonder how obfuscated such drawings can be. We define obf(G), the obfuscation complexity of G, to be the maximum number of edge crossings in a drawing of G. Relating obf(G) to the distribution of vertex degrees in G, we show an efficient way of constructing a drawing of G with at least obf(G)/3 edge crossings. We prove bounds (δ(G)2/24−o(1))n2≤obf(G)<3n2 for an n-vertex planar graph G with minimum vertex degree δ(G)≥2. The shift complexity of G, denoted by shift(G), is the minimum number of vertex shifts sufficient to eliminate all edge crossings in an arbitrarily obfuscated drawing of G (after shifting a vertex, all incident edges are supposed to be redrawn correspondingly). If δ(G)≥3, then shift(G) is linear in the number of vertices due to the known fact that the matching number of G is linear. However, in the case δ(G)≥2 we notice that shift(G) can be linear even if the matching number is bounded. As for computational complexity, we show that, given a drawing D of a planar graph, it is NP-hard to find an optimum sequence of shifts making D crossing-free." @default.
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- W2080201242 date "2008-05-01" @default.
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- W2080201242 title "On the obfuscation complexity of planar graphs" @default.
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- W2080201242 doi "https://doi.org/10.1016/j.tcs.2008.02.032" @default.
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