3 research outputs found
Note on minimally -rainbow connected graphs
An edge-colored graph , where adjacent edges may have the same color, is
{\it rainbow connected} if every two vertices of are connected by a path
whose edge has distinct colors. A graph is {\it -rainbow connected} if
one can use colors to make rainbow connected. For integers and
let denote the minimum size (number of edges) in -rainbow connected
graphs of order . Schiermeyer got some exact values and upper bounds for
. However, he did not get a lower bound of for . In this paper, we improve his lower bound of
, and get a lower bound of for .Comment: 8 page