graph coloring

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graph coloring

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According to Hogg, the ultimate test is that of "colourability": "the more elaborate the regulatory scheme, the more likely the court will classify [it] as regulatory rather than criminal." (178)
Apart from that, a few minor quibbles arise: The book does not directly discuss interpretative principles used by the courts in division of powers cases, such as pith and substance, double aspect, singling out and colourability; the delegation of legislative powers is touched on but not really dealt with outside the two case studies; and the complex interaction of constitutional conventions and their use in court cases are also unexplored in a text that ties many other political dimensions into the constitution.
It follows that the S-weight colourability of a graph is not only dependent on the size of S but also on the particular elements of S.
Let us start by considering the 2-weight colourability of a simple class of graphs--paths.
Returning to Problem 1, we state the following conjecture, due to Karonski, Luczak, and Thomason [KLT04], which motivates most of the known results on the {1, ..., k}-weight colourability of graphs.
These results provide building blocks for our results on the weight colourability of bipartite graphs in Section 3 and of other general classes of graphs, particularly direct products of graphs, in Section 4.
The following lemma establishes that we may contract long threads in a way that maintains weight colourability.
The product is currently UL-recognized only in black formulations, but the company says its FR formulation is expected to provide a broader range of colourability than brominated FR systems and non-halogenated ones based on red phosphorus which typically permit only dark colours.