Full complexity classification for three b- and fall-coloring problems in H-free graphs plus a separation showing b-Chromatic Number can be NP-hard while Tight b-Chromatic Number is P-time solvable for some H.
Laskar and Jeremy Lyle
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Optimal b-Colourings and Fall Colourings in $H$-Free Graphs
Full complexity classification for three b- and fall-coloring problems in H-free graphs plus a separation showing b-Chromatic Number can be NP-hard while Tight b-Chromatic Number is P-time solvable for some H.