Displaying similar documents to “The neighborhood complex of an infinite graph.”

Simple Graphs as Simplicial Complexes: the Mycielskian of a Graph

Piotr Rudnicki, Lorna Stewart (2012)

Formalized Mathematics

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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 similar material is in [15].

Derived graphs of some graphs

Sudhir R. Jog, Satish P. Hande, Ivan Gutman, S. Burcu Bozkurt (2012)

Kragujevac Journal of Mathematics

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A Note on the Seven Bridges of Königsberg Problem

Adam Naumowicz (2014)

Formalized Mathematics

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In this paper we account for the formalization of the seven bridges of Königsberg puzzle. The problem originally posed and solved by Euler in 1735 is historically notable for having laid the foundations of graph theory, cf. [7]. Our formalization utilizes a simple set-theoretical graph representation with four distinct sets for the graph’s vertices and another seven sets that represent the edges (bridges). The work appends the article by Nakamura and Rudnicki [10] by introducing the...