Clique partitions of chordal graphs: quantitative stability and sharp eventual bounds
A Lean 4 / Mathlib formalization of the chordal results of the author's preprint "Clique partitions with rooted simplicial defect: quantitative stability and sharp eventual bounds" (Erdős #81 series, Paper IV). With M(n) = ⌊n(n+1)/6⌋: there is b such that every chordal graph on n vertices has a clique partition into pieces of order at most four with at most M(n) + b pieces (Theorem A); for n large every chordal graph on n vertices has one with at most M(n) pieces, and some chordal graph on n vertices has one with exactly M(n) pieces that is optimal among all clique partitions (Theorem B, the…
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