Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph
نویسندگان
چکیده
منابع مشابه
Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph
Harary [10, p. 7] claims that Veblen [20, p. 2] first suggested to formalize simple graphs using simplicial complexes. We have developed basic terminology for simple graphs as at most 1-dimensional complexes. We formalize this new setting and then reprove Mycielski’s [12] construction resulting in a triangle-free graph with arbitrarily large chromatic number. A different formalization of simila...
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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 the...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2012
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-012-0019-8