Time: 14h00, Thursday, June 11, 2020

Location: Room 612, Building A6, Institute of Mathematics

Abstract: Recently, the concepts of connection problems are introduced in graph theory. Let $G$ be a nontrivial connected graph on which an edge-colouring $c:E(G)rightarrowlbrace 1,2,ldots,nrbrace, ninmathbb{N}$, is defined, where adjacent edges may be coloured the same. 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 two 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 results on $mathcal{P}$ connection number and size of graphs.