The list chromatic number $χ_{L} (G)$ is defined to be the minimal $k$ such that for any assignment of a list of $k$ colours to each vertex of $G$ (perhaps different lists for different vertices) a colouring of each vertex by a colour on its list can be chosen such that adjacent vertices receive distinct colours.Determine the minimal number of vertices $n (k)$ of a bipartite graph $G$ such that $χ_{L} (G) > k$ .

Worked, still open.

graph theory · open · possible · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

[ n(k)=\min{|V(G)|:G\text{ is bipartite and }\chi_L(G)>k}, ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

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