Georgia Institute of Technology College of Sciences

A Roman dominating function of a graph G is a function f which maps V(G) to {0, 1, 2} such that whenever f(v)=0, there exists a vertex u adjacent to v such that f(u)=2. The weight of f is w(f) = \sum_{v \in V(G)} f(v). The Roman domination number \gamma_R(G) of G is the minimum weight of a Roman dominating function of G. Chambers, Kinnersley, Prince and West conjectured that \gamma_R(G) is at most the ceiling 2n/3 for any 2-connected graph G of n vertices. In this talk, we will give counter-examples to the conjecture, and proves that \gamma_R(G) is at most the maximum among the ceiling of 2n/3 and 23n/34 for any 2-connected graph G of n vertices. This is joint work with Gerard Jennhwa Chang.