On some connection problems

Tóm tắt báo cáo

In the last years, the connection concepts of connected graphs appeared in graph theory and received many attentions. Let $G$ be a connected and edge-coloured graph. A path $P$ in the graph $G$ is called \emph{$\mathcal{P}$ path} if its edges are assigned colours with $\mathcal{P}$ property. The edge-coloured graph $G$ is \emph{$\mathcal{P}$ connected} if every pair vertices are connected by at least one $\mathcal{P}$ path in $G$. The \emph{$\mathcal{P}$ connection number} of the graph $G$, denoted by $\mathcal{P}(G)$, is the smallest number of colours in order to make it $\mathcal{P}$ connected. In our talk, we will present some result on this topic.