Autour de problèmes de plongements de graphes

Abstract : This Ph.D. manuscript is built around the notion of graph embedding. An embedding of a graph G is an application mapping the vertices of G to elements of another structure, and preserving some properties of G. There are two types of embeddings. The combinatorial embeddings map the vertices of a graph G to the vertices of a graph H. The usual property that is preserved is the adjacency between vertices. In this thesis, we consider the isometric embeddings, preserving in addition the distances between vertices. We give some structural characterizations for families of graphs isometrically embeddable in hypercubes or Hamming graphs. The topological embeddings aim at drawing a graph G on some surface. Vertices are mapped to distinct points of the surface and the edges are represented by continuous curves linking these points. Is it possible to draw a graph G so that the edges do not cross eachother ? If not, what is the minimum number of crossings of a drawing of G ? We deal with these questions on different surfaces, or in relation with some graph operations as direct product or zip product.
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Theses
Mathematics [math]. Université Joseph-Fourier - Grenoble I, 2009. French


https://tel.archives-ouvertes.fr/tel-00401226
Contributor : Laurent Beaudou <>
Submitted on : Thursday, July 2, 2009 - 4:38:30 PM
Last modification on : Thursday, July 2, 2009 - 4:42:32 PM

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Laurent Beaudou. Autour de problèmes de plongements de graphes. Mathematics [math]. Université Joseph-Fourier - Grenoble I, 2009. French. <tel-00401226>

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