The Erdos-Hajnal High-Girth Subgraph Conjecture
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in polynomial edge-density regimes; the general question remains open
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combinatorics / Graph theory
The Erdos-Hajnal High-Girth Subgraph Conjecture
Erdos and Hajnal asked whether $h_r(G) = \max\{\chi(H) : H \subseteq G,\ \mathrm{girth}(H) \ge r\}$ tends to infinity as $\chi(G)$ does, for every fixed $r \ge 4$. It does in every fixed polynomial edge-density regime.
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Erdos and Hajnal asked whether $h_r(G) = \max\{\chi(H) : H \subseteq G,\ \mathrm{girth}(H) \ge r\}$ tends to infinity as $\chi(G)$ does, for every fixed $r \ge 4$. It does in every fixed polynomial edge-density regime.
in polynomial edge-density regimes; the general question remains open
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