  In an attempt to understanding the complexity of the independent set problem,
Chv{\'a}tal defined t-perfect graphs. While a full characterization of this
class is still at large, progress has been achieved for claw-free graphs [Bruhn
and Stein, Math.\ Program.\ 2012] and $P_{5}$-free graphs [Bruhn and Fuchs,
SIAM J.\ Discrete Math.\ 2017]. We take one more step to characterize fork-free
t-perfect graphs, and show that they are strongly t-perfect and
three-colorable. We also present polynomial-time algorithms for recognizing and
coloring these graphs.
