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On extremal properties of minimal Ramsey graphs and cross intersecting families
Citation Link: https://doi.org/10.15480/882.4979
Publikationstyp
Doctoral Thesis
Date Issued
2023
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2023-02-28
Institut
TORE-DOI
Citation
Technische Universität Hamburg (2023)
This thesis is divided into four parts, three out of which investigate the behaviour of
the set of minimal Ramsey graphs for a particular graph. In the rst part we investigate
the phenomena of Ramsey simplicity for random graphs, Gn,p. We show the existence of
a threshold value for the number of colours for which a given graph is Ramsey simple and
determine various bounds for it. In the second part we de ne and analyse the abundance
properties of graphs. We exhibit many in nite classes of graphs which are abundant for a
certain number of colours. The third part of the thesis provides an evidence of asymmetric
pairs of graphs which are Ramsey equivalent. In the last part of this thesis we determine
the maximum sum of the sizes of r-cross t-intersecting families in various settings.
the set of minimal Ramsey graphs for a particular graph. In the rst part we investigate
the phenomena of Ramsey simplicity for random graphs, Gn,p. We show the existence of
a threshold value for the number of colours for which a given graph is Ramsey simple and
determine various bounds for it. In the second part we de ne and analyse the abundance
properties of graphs. We exhibit many in nite classes of graphs which are abundant for a
certain number of colours. The third part of the thesis provides an evidence of asymmetric
pairs of graphs which are Ramsey equivalent. In the last part of this thesis we determine
the maximum sum of the sizes of r-cross t-intersecting families in various settings.
Subjects
Minimum degrees
minimal Ramsey graphs
r-cross t-intersecting families
DDC Class
500: Naturwissenschaften
510: Mathematik