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Talk:Frequency partition of a graph

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This is an old revision of this page, as edited by Gandalf61 (talk | contribs) at 10:28, 18 March 2008 (→Errors: expand). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Can you create this subject on Wikipedia ? It is good to have a subject "Frequency Partition" rather than writing it on a different page. It is related to the subject Degree sequence in Graph Theory. Let me know what is the best way to write about "Frequency Partition" in Graph Theory. --Tangi-tamma (talk) 16:52, 16 March 2008 (UTC)[reply]

Administrators should have some patience and wait for some time if they do not follow. --Tangi-tamma (talk) 17:34, 16 March 2008 (UTC)[reply]

I have tagged for context again as the article makes no attempt to define "frequency partition". Please try to write a sentence which starts with "In graph theory, the frequency partition of a graph is..." and put that at the start of the article. This may be obvious to you but it will provide introduction and context for readers who are not yet familiar with the subject and are reading the article to find out about it. You might also like to reuse one or more the diagrams on Degree (graph theory) to illustrate the subject. --DanielRigal (talk) 20:26, 16 March 2008 (UTC)[reply]

Errors

1. The article says "Chinn proved that given any partition p= f1+f2+...+fk of an integer p > 1, other than p = 1+1+1+...+1, there is at least one (connected) graph having this partition as its frequency partition". Not sure what Chinn may have proved, but it certainly wasn't this result, which is incorrect. Counterexamples:

  • There is no graph with frequency partition (1,2) i.e. one vertex with degree 1 and two vertices with degree 2.
  • There is no connected graph with frequency partition (4,1) i.e. four vertices with degree 1 and one vertex with degree 2.

I suggest this sentence should be either fixed or removed.

2. The article says "there can be several degree sequences compatible with a given frequency partition". Unless I have misunderstood how frequency partitions work, this cannot be correct. Surely the degree sequence can be simply read off from the frequency partition - a graph with frequency partition (1,4,1) must have degree sequence (1, 2, 2, 2, 2, 3). How can there be any ambiguity in translating from frequency partition back to degree sequence ? Gandalf61 (talk) 10:28, 18 March 2008 (UTC)[reply]

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