A note on the 3-rainbow index of $K_{2,t}$

Abstract

A tree $T$, in an edge-colored graph $G$, is called {\em a rainbow tree} if no two edges of $T$ are assigned the same color. For a vertex subset $S\in V(G)$, a tree that connects $S$ in $G$ is called an $S$-tree. A {\em $k$-rainbow coloring} of $G$ is an edge coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a rainbow $S$-tree $T$ in $G$. The minimum number of colors needed in a $k$-rainbow coloring of $G$ is the {\em $k$-rainbow index of $G$}, denoted by $r{x}_k(G)$. In this paper, we obtain the exact values of $r{x}_3(K_{2,t})$ for any $t\ge 1$.

6 pages 4 figures

Cited by in corpus (1)

• The 3-rainbow index of graph operations