Faktorizace kompletních grafů na housenky s průměrem 6 a třemi bohatými vrcholy

Abstract

The goal of this bachelor thesis is to find at least one unknown infinite class of caterpillars with diameter 6 that factorizes a complete graph of order 2n, where n is odd. We focus into caterpillars with exactly three vertices of degree at least 3. The caterpillars, which we investigate, contain a vertex of degree n (it is a maximum degree of vertex that allows factorization of K2n) and vertex of degree 3. A part of 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 diameter 6.