本文主要是介绍7.9 证明：$\chi(G-e) = \min \{\chi(G),\chi(G\cdot e) \}$，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
7.9 证明： χ ( G − e ) = min { χ ( G ) , χ ( G ⋅ e ) } \chi(G-e) = \min \{\chi(G),\chi(G\cdot e) \} χ(G−e)=min{χ(G),χ(G⋅e)}
证：
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色多项式的递推公式： P k ( G ) = P k ( G − e ) − P k ( G ⋅ e ) P_k(G) =P_k(G-e)-P_k(G\cdot e) Pk(G)=Pk(G−e)−Pk(G⋅e)
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χ ( G − e ) = min { k ∣ P k ( G − e ) ≠ 0 } = min { k ∣ P k ( G ) + P k ( G ⋅ e ) ≠ 0 } = min { χ ( G ) , χ ( G ⋅ e ) } \begin{aligned} \chi(G-e) &= \min\{k | P_k(G-e) \ne 0 \} \\ &= \min\{k | P_k(G)+P_k(G\cdot e) \ne 0 \} \\ &= \min \{\chi(G),\chi(G\cdot e) \} \end{aligned} χ(G−e)=min{k∣Pk(G−e)=0}=min{k∣Pk(G)+Pk(G⋅e)=0}=min{χ(G),χ(G⋅e)}
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