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Formalized Mathematics

2011 | 19 | 1 | 27-34

The Mycielskian of a Graph

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Abstrakty

EN
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.

27-34

wydano
2011-01-01
online
2011-07-18

Twórcy

autor
• University of Alberta, Edmonton, Canada
autor
• University of Alberta, Edmonton, Canada

Bibliografia

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