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There seems to be a mistake in the last paragraph of "Examples". Having a regular connected component is not a nessecary condition for the graph to be degenerate of the maximum degree. In the source either it is a typo or more likely col(G) doesn't actually stand for the degeneracy of G. To correct,
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one could state, "More strongly, the degeneracy of a graph equals its maximum vertex degree if and only if at least one subgraph of G is regular of maximum degree. For all other graphs, the degeneracy is strictly less than the maximum degree."
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https://web.archive.org/web/20061111032123/http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/EmergenceRandom_Science%20286%2C%20509-512%20%281999%29.pdf
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I think they are off by one. Degeneracy d means you can greedily color it with d+1 colors, as explained in the body of the article. —
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What is meant by "essentially the same"? Are the numbers equivalent or not? If they are not equivalent, what is the difference?
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https://web.archive.org/web/20110722065122/http://www.dia.uniroma3.it/~patrigna/papers/files/ASGraphDynamicAnalysis.pdf
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I think it would make the article more clear to either remove the word 'essentially' or explain the differences.
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