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A graph is Hamiltonian if it contains a spanning cycle. In this paper, we examine the hamiltonicity of the Cartesian product of a tree with a path. We offer sufficient conditions for the Cartesian product of a tree with a path to be Hamiltonian.

Dokažemo, da je vsaka največja neodvisna množica v direktnem produktu sodega cikla ali lihe poti s poljubnim grafom $G$ unija množic $(A \times B$) in $(C \times D$), kjer sta $A$ in $C$ podmnožici cikla oziroma poti, ter $B$ in $D$ podmnožici grafa $G$. Prav tako diskutiramo strukturo največjih neo ...

Doktorska disertacija obravnava nekatere rezultate na grafovskih produktih. V uvodu bomo na kratko predstavili vsebino doktorske disertacije in ponovili nekatere osnovne pojme teorije grafov, ki jih bomo uporabljali v nadaljevanju. Prva tema, ki jo bomo predstavili so neodvisne množice v direktnem p ...

A path factor in a graph G is a factor of G in which every component is a path on at least two vertices. Let be the Cartesian product of a tree T and a path on n vertices. Kao and Weng [11] proved that is hamiltonian if T has a path factor, n is an even integer and . They conjectured that for every ...