TOPGRAPHS · Graph theory and general topology: foundations, infinite graphs and beyond

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Project objective

In spite of the traditional gap between graph theory and topology, it is possible to view a graph as a (possibly finite) non-trivial topological object.With respect to this novel topology, the ground set consists of the vertices and edges of the graph, so that an edge is as much of a 'point' in the space as a vertex is, in contrast with the traditional way of modelling a graph as a one-dimensional cell-complex.This topological construction reduces graph-theoretic connectedness directly to connectedness in the sense of abstract topology, and is the basis for the recent work of Richter and Vella. This work generalizes standard results from graph theory to a certain class of topological spaces, and simplifies and generalizes the related recent work of Dieste l and Kuhn.Since the new perspective translates the notions of graph theory into topological concepts, it brings together the fields of graph theory and point-set topology in a fundamental way, and opens up an array of questions much wider in scope than the issues addressed so far.The objectives of this project are inspired by the potential to bring this new approach to bear on the central tenets of finite and infinite graph theory, including Menger's Theorem and graph minors, and the related field of matroid theory.

Original text from CORDIS.

Participants

• DANMARKS TEKNISKE UNIVERSITET (TECNICAL UNIVERSITY OF DENMARK) · KGS. LYNGBYCoordinatorCity levelDenmark

Links

• View on CORDIS