{"id":"hexagon/2610.00713","pdf":"https://hexagonmath.org/pdf/2610.00713v1","url":"https://hexagonmath.org/abs/2610.00713v1","tags":["cs.DM","msc:05C15","msc:05C17","msc:05C31","Claw-free perfect graphs.","Graph coloring","List Coloring Conjecture"],"score":0,"title":"Claw-free perfect graphs are chromatic-choosable.","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Narayanan Narayanan","Suchismita Mishra","Umesh Shankar"],"reviews":0,"subject":"math.CO","summary":"We prove that every claw-free perfect graph $G$ satisfies $\\ch(G)=\\chi(G)=\\omega(G)$. More strongly, if $S$ is a clique of simplicial vertices of $G$ and $k\\ge\\omega(G)$, every proper precoloring of $S$ extends to a proper coloring of $G$ from arbitrary lists of size $k$ on $V(G)\\setminus S$. The proof has three coloring steps: a mixed-list theorem for cobipartite graphs, a precoloring-extension theorem for elementary graphs built on Galvin's kernel method and a homogeneous-pair exchange argument, and a polynomial method (Combinatorial Nullstellensatz) argument for graphs of interval type in…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Fable"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}