File:Grötzsch graph.svg
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Summary[edit]
Very hastily drawn image of the fourth Mycielski graph. Mycielski proved in 1955 that for every there is a graph with chromatic number k that contains no triangle subgraphs, that is, whose maximal clique size is just 2. (This was also proved by A. A. Zykov, Mat. Zb. 24, (1949), 2, 163-183 (in Russian) and by "Blanche Descartes" (W. T. Tutte) Amer. Math. Monthly 61, (1954) p. 352.) The chromatic number of this graph is 4.
A simple construction of triangle-free graphs of any chromatic number is this. Start with a -chromatic graph G with no triangle. Take copies of G. Form all sets consisting of 1 node from each copy. Connect the nodes in each of these sets to a new node. The resulting graph is triangle-free and -chromatic.
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This work has been released into the public domain by its author, Bkell. This applies worldwide. In some countries this may not be legally possible; if so: |
Original upload log[edit]
date/time | username | resolution | size | edit summary | |
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09:37, 17 December 2006 | User:Booyabazooka | <a href="http://upload.wikimedia.org/wikipedia/commons/5/5e/Fourth_Mycielski_graph.svg"><img alt="Thumbnail for version as of 09:37, 17 December 2006" src="http://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Fourth_Mycielski_graph.svg/120px-Fourth_Mycielski_graph.svg.png" width="120" height="115" border="0" /></a> | 480×460 | 8 KB | Prettier version requested... how's this? |
10:33, 3 July 2006 | User:Bkell | <a href="http://upload.wikimedia.org/wikipedia/commons/archive/5/5e/20061217093723%21Fourth_Mycielski_graph.svg"><img alt="Thumbnail for version as of 10:33, 3 July 2006" src="http://upload.wikimedia.org/wikipedia/commons/thumb/archive/5/5e/20061217093723%21Fourth_Mycielski_graph.svg/120px-Fourth_Mycielski_graph.svg.png" width="120" height="120" border="0" /></a> | 700×700 | 6 KB | Very hastily drawn image of the fourth Mycielski graph. Mycielski proved in 1955 that for every <math>k\ge1</math> there is a graph with chromatic number ''k'' that contains no triangle subgraphs, that is, whose maximal clique size is just 2. The chromati |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:14, 21 November 2008 | 480 × 460 (8 KB) | BetacommandBot (talk | contribs) | move approved by: User:Deadstar This image was moved from Image:Fourth Mycielski graph.svg == Summary == Very hastily drawn image of the fourth Mycielski graph. Mycielski proved in 1955 that for every <math>k\ge1</math> there is a graph with c |
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