Chromatic Roots and Hamiltonian Paths

We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t0=23+13 26 +6 33+13 26 +6 33=1.29559…,then the graph has no hamiltonian path. This result is best possible in the sense that it becomes false if t0 is replaced by any larger number.