Category:Tutte's Wheel Theorem

This category contains pages concerning Tutte's Wheel Theorem:

Every $3$-connected graph can be obtained by the following procedure:

• Start with $G_0 := K_4$
• Given $G_i$ pick a vertex $v$
• Split into $v'$ and $v' '$ and add edge $\set {v', v' '}$

This procedure directly follows from the theorem:

A graph $G$ is $3$-connected (A) if and only if there exists a sequence $G_0, G_1, \dotsc, G_n$ of graphs with the following properties (B):

• $G_0 = K_4$ and $G_n = G$
• $G_{i + 1}$ has an edge $e = x y$ with $\map \deg x, \map \deg y \ge 3$ and $G_i = G_{i + 1} / e$ for every $i < n$.