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Pole DC | Wartość | Język |
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dc.contributor.author | Rudnicki, Piotr | - |
dc.contributor.author | Stewart, Lorna | - |
dc.date.accessioned | 2015-12-06T19:04:20Z | - |
dc.date.available | 2015-12-06T19:04:20Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Formalized Mathematics, Volume 19, Issue 1, 2011, Pages 27-34 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.issn | 1898-9934 | - |
dc.identifier.uri | http://hdl.handle.net/11320/3592 | - |
dc.description.abstract | Let ω(G) and χ(G) be the clique number and the chromatic number of a graph G. Mycielski [11] presented a construction that for any n creates a graph Mn which is triangle-free (ω(G) = 2) with χ(G) > n. The starting point is the complete graph of two vertices (K2). M(n+1) is obtained from Mn through the operation μ(G) called the Mycielskian of a graph G. We first define the operation μ(G) and then show that ω(μ(G)) = ω(G) and χ(μ(G)) = χ(G) + 1. This is done for arbitrary graph G, see also [10]. Then we define the sequence of graphs Mn each of exponential size in n and give their clique and chromatic numbers. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.title | The Mycielskian of a Graph | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/v10037-011-0005-6 | - |
dc.description.Affiliation | Rudnicki Piotr - University of Alberta, Edmonton, Canada | - |
dc.description.Affiliation | Stewart Lorna - University of Alberta, Edmonton, Canada | - |
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dc.description.references | M. Larsen, J. Propp, and D. Ullman. The fractional chromatic number of Mycielski's graphs. Journal of Graph Theory, 19:411-416, 1995, doi: 10.1002/jgt.3190190313 | - |
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dc.description.references | Piotr Rudnicki. Dilworth's decomposition theorem for posets. Formalized Mathematics, 17(4):223-232, 2009, doi: 10.2478/v10037-009-0028-4. | - |
dc.description.references | Wojciech A. Trybulec and Grzegorz Bancerek. Kuratowski - Zorn lemma. Formalized Mathematics, 1(2):387-393, 1990. | - |
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Występuje w kolekcji(ach): | Formalized Mathematics, 2011, Volume 19, Issue 1 |
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