Rainbow connection in $3$-connected graphs

Details Rainbow connection in $3$-connected graphs Rainbow connection in $3$-connected graphs

2010-10-29

arxiv.org/abs/1010.6131v1

Mathematics

Combinatorics

7 pages

Scientific paper

An edge-colored graph $G$ is rainbow connected if any two vertices are
connected by a path whose edges have distinct colors. The rainbow connection
number of a connected graph $G$, denoted by $rc(G)$, is the smallest number of
colors that are needed in order to make $G$ rainbow connected. In this paper,
we proved that $rc(G)\leq 3(n+1)/5$ for all $3$-connected graphs.

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