从Neel到NPC：为小世界着色
From Neel to NPC: Colouring Small Worlds
摘要：
在这份说明中，我们提出的着色问题的小世界图重新布线的正方形，三角形，和两种立方（与协调数5和6）格。当重布线参数p趋于1时，我们发现具有相应连通性的随机图的行为的预期交叉。然而，对于立方晶格，在p=0附近存在一个区域，在该区域中，图是并列的。原则上，这可以用作解决现实世界着色或调度问题的额外启发式。连通度为5且p ~ 0.1的小世界提供了一个有趣的图系综，其着色性很难确定。对于正方形格子，我们得到了良好的数据崩溃绘制的分数的color-graphs对重新缩放的参数参数$p N^{-ν}$与$ν= 1.35$。对于配位数为5或6的格点的数据，不能得到这样的坍缩。
英文摘要：
In this note, we present results for the colouring problem on small world graphs created by rewiring square, triangular, and two kinds of cubic (with coordination numbers 5 and 6) lattices. As the rewiring parameter p tends to 1, we find the expected crossover to the behaviour of random graphs with corresponding connectivity. However, for the cubic lattices there is a region near p=0 for which the graphs are colourable. This could in principle be used as an additional heuristic for solving real world colouring or scheduling problems. Small worlds with connectivity 5 and p ~ 0.1 provide an interesting ensemble of graphs whose colourability is hard to determine. For square lattices, we get good data collapse plotting the fraction of colourable graphs against the rescaled parameter parameter $p N^{-ν}$ with $ν= 1.35$. No such collapse can be obtained for the data from lattices with coordination number 5 or 6.
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