Faktorizace kompletních grafů na housenky s průměrem 6

Abstract

The goal of this bachelor thesis is to find an unknown infinite class of caterpillars with a diameter $6$ that factorizes a complete graph of order $2n$ (where $n$ is odd), an implementation of a programme for finding blended labeling of spanning trees, and an implementation of a programme which will work as an input into the software used for parallel search for factorizations of complete graphs. A part of the thesis is a citation of known results for factorizations of complete graphs into caterpillars with diameters $4$ and $5$. Further included is a citation of necessary conditions and sufficient conditions for factorizations of complete graphs into spanning trees and their applications for characterization of chosen infinite class of caterpillars with a diameter $6$.