On Fork-Free t-Perfect Graphs

In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t-perfect graphs. While a full characterization of this class remains open, important progress has been made for claw-free graphs [Bruhn and Stein, Math. Program. 2012] and (Formula presented.) -free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]. We take a further step by characterizing fork-free t-perfect graphs and showing that they are strongly t-perfect and 3-colorable. We also give polynomial-time algorithms for recognizing and coloring fork-free t-perfect graphs.