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I think that written like this, the characterization of chordal graphs with intersection graphs is incorrect. If we read the sentence, we have the impression that chordal=subtree overlap, which is false. I guess it should be intersecting subtrees, and not overlaping subtrees. (see F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combinatorial Th. (B), 16(1974)47-56.)
I don't think the chromatic number of a chordal graph equals its clique number. Consider K_n and attach a dangling edge to one of its vertices. It is chordal, its clique number is n and its chromatic number is n+1. —Preceding
unsigned comment added by
68.49.197.167 (
talk)
05:10, 17 July 2008 (UTC)
Must chords always be a single edge? What about the segment A-B-C in this graph? If this is not a chord, then what is it called?
O-O-A-O-O / | \ O B O \ | / O-O-C-O-O
If A-B-C is not a chord, then does that mean that all 3 cycles in this graph are chord-less, even though one of them is obviously divided by the other two? —Preceding unsigned comment added by 76.27.92.148 ( talk) 12:50, 5 August 2010 (UTC)
The reference for "A graph is chordal if and only if it has a perfect elimination" doesn't contain the word chordal nor perfect elimination, therefore my question if the reference is correct. Thanks for clarifying. 158.143.75.80 ( talk) 15:16, 5 July 2014 (UTC)
This article is rated B-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
I think that written like this, the characterization of chordal graphs with intersection graphs is incorrect. If we read the sentence, we have the impression that chordal=subtree overlap, which is false. I guess it should be intersecting subtrees, and not overlaping subtrees. (see F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combinatorial Th. (B), 16(1974)47-56.)
I don't think the chromatic number of a chordal graph equals its clique number. Consider K_n and attach a dangling edge to one of its vertices. It is chordal, its clique number is n and its chromatic number is n+1. —Preceding
unsigned comment added by
68.49.197.167 (
talk)
05:10, 17 July 2008 (UTC)
Must chords always be a single edge? What about the segment A-B-C in this graph? If this is not a chord, then what is it called?
O-O-A-O-O / | \ O B O \ | / O-O-C-O-O
If A-B-C is not a chord, then does that mean that all 3 cycles in this graph are chord-less, even though one of them is obviously divided by the other two? —Preceding unsigned comment added by 76.27.92.148 ( talk) 12:50, 5 August 2010 (UTC)
The reference for "A graph is chordal if and only if it has a perfect elimination" doesn't contain the word chordal nor perfect elimination, therefore my question if the reference is correct. Thanks for clarifying. 158.143.75.80 ( talk) 15:16, 5 July 2014 (UTC)