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· 1997

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CONDITIONAL 1

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The asymptotic $\chi$-boundedness of hereditary families

math.CO · 2025-06-01 · conditional · novelty 7.0

For every tree T, almost all T-free graphs satisfy chi=omega, and for every cycle C_k except C_6, almost all C_k-free graphs satisfy chi=omega; C_6-free graphs are asymptotically chi-bounded with f(w)=(1+o(1))w^2/log w.

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  • The asymptotic $\chi$-boundedness of hereditary families math.CO · 2025-06-01 · conditional · none · ref 3

    For every tree T, almost all T-free graphs satisfy chi=omega, and for every cycle C_k except C_6, almost all C_k-free graphs satisfy chi=omega; C_6-free graphs are asymptotically chi-bounded with f(w)=(1+o(1))w^2/log w.