[習題] 4.14(b) 題目似乎有誤.
It say that for any $x\in V(G)$,
show that $C-x$ satisties Tutte's condition:
For $S\subseteq V(C-x)$, $o((C-x)-S)\leq |S|$.
If $x\notin V(C)$ for some odd component $C$,
and when we check the case of $S=\emptyset$,
then $o((C-x)-S)=o(C-S)=o(C)=1>0=|S|$ and hence it fails.
Even if $x\in V(C)$ for some even component $C$,
and also when we check the case of $S=\emptyset$,
then $o((C-x)-S)=o(C-x)\geq 1>0=|S|$ and hence it fails, too.
In my opinion, it should be $x\in V(C)$ for odd component $C$,
and it still can be used to prove Tutte's theorem.
p.s. Here I use latex lanquage:
\in := belongs to,
\notin := not belongs to
\subseteq :=contained in
\leq :less or equal
\emptyset := empty set
※ 編輯: killyou 來自: 140.112.231.114 (12/04 23:37)
討論串 (同標題文章)
以下文章回應了本文：
完整討論串 (本文為第 1 之 2 篇)：