Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.815689
Title: Two problems in graph theory
Author: Kučera, Stanislav
ISNI:       0000 0004 9358 8519
Awarding Body: London School of Economics and Political Science (LSE)
Current Institution: London School of Economics and Political Science (University of London)
Date of Award: 2019
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Abstract:
In the thesis we study two topics in graph theory. The first one is concerned with the famous conjecture of Hadwiger that every graph G without a minor of a complete graph on t +1 vertices can be coloured with t colours. We investigate how large an induced subgraph of G can be, so that the subgraph can be coloured with t colours. We show that G admits a t-colourable induced subgraph on more than half of its vertices. Moreover, if such graph G on n vertices does not contain any triangle, we show it admits a t-colourable induced subgraph on at least 4n=5 vertices and show even better bounds for graphs with larger odd girth. The second topic is a variant of a well-known two player Maker-Breaker connectivity game in which players take turns choosing an edge in each step in order to achieve their respective goals. While a complete characterisation is known for the connectivity game in which both players choose a single edge, much less is known in all other cases. We study the variant in which both players choose two edges, or more generally, the variant in which the first player decides whether both players choose one or two edges in the next round.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.815689  DOI:
Keywords: QA Mathematics
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