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  "body": "\n## Statement\n\nIn graph theory, the **Gyárfás–Sumner conjecture** says that for any fixed [[tree|062D9KXJB1]] $T$, the class of all $T$-free graphs is $\\chi$-bounded; that is, every graph that contains neither $T$ nor $K_t$ as an [[induced subgraph|0EREPBVG2G]] can be [[properly colored|0NCPXH194Y]] using a constant number of colors, depending only on $T$ and $t$. Equivalently, it says that every $K_t$-free graph $G$ contains any arbitrarily chosen tree $T$ (as an induced subgraph), as long as $\\chi(G)$ is large enough. It is named after András Gyárfás and David Sumner, who formulated it independently in 1975 and 1981 respectively. It remains unproven.\n",
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