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Existence and enumeration of spanning structures in sparse graphs and hypergraphs
Citation Link: https://doi.org/10.15480/882.1310
Publikationstyp
Doctoral Thesis
Date Issued
2016
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2016-06-30
Institut
TORE-DOI
This thesis examines the robustness of sparse graphs and hypergraphs with respect to containing copies of given spanning subgraphs. In particular, we prove analogues of the bandwidth theorem for random and pseudorandom graphs, as well as a Dirac-type theorem for Hamilton Berge cycles in random r-uniform hypergraphs. Furthermore, we determine conditions for the existence of rainbow matchings in edge-coloured multigraphs and study the number of spanning trees in graphs chosen uniformly at random from subfamilies of series-parallel graphs.
Subjects
Extremale Graphentheorie, analytische Kombinatorik, zufällige und pseudozufällige Graphen und Hypergraphen, lokale Resilienz, Regenbogenmatchings
DDC Class
510: Mathematik
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Dissertation.pdf
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1.37 MB
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