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Displaying similar documents to “Dotted links, Heegaard diagrams, and colored graphs for PL 4-manifolds.”

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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3-manifold spines and bijoins.

Luigi Grasselli (1990)

Revista Matemática de la Universidad Complutense de Madrid

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We describe a combinatorial algorithm for constructing all orientable 3-manifolds with a given standard bidimensional spine by making use of the idea of bijoin (Bandieri and Gagliardi (1982), Graselli (1985)) over a suitable pseudosimplicial triangulation of the spine.