For chordal graphs, k-colorings with k ≥ d+4 admit single-vertex recoloring transformations of length at most f(Δ)·n, with a linear-time algorithm to compute the sequence.
20 Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
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Linear transformations between colorings in chordal graphs
For chordal graphs, k-colorings with k ≥ d+4 admit single-vertex recoloring transformations of length at most f(Δ)·n, with a linear-time algorithm to compute the sequence.