Talk:Degeneracy (graph theory)

Examples

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, 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." — Preceding unsigned comment added by 82.130.77.94 (talk) 14:22, 8 December 2016 (UTC)[reply]

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What is meant by 'essentially the same'?

In the article, there is the following line:

"Degeneracy is also known as the k-core number, width, and linkage, and is essentially the same as the coloring number or Szekeres–Wilf number (named after Szekeres and Wilf (1968))."

What is meant by "essentially the same"? Are the numbers equivalent or not? If they are not equivalent, what is the difference?

I think it would make the article more clear to either remove the word 'essentially' or explain the differences. BranAndSceolan (talk) 08:31, 5 July 2023 (UTC)[reply]

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. —David Eppstein (talk) 18:26, 5 July 2023 (UTC)[reply]