Two problems in graph theory

Stanislav Kučera
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...
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