Construction Sequences and Certifying 3-Connectedness
نویسنده
چکیده
Tutte proved that every 3-connected graph on more than 4 nodes has a contractible edge. Barnette and Grünbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to the K4 can be computed in O(|V | ) time by extending Barnette and Grünbaum’s theorem. As an application, we derive a certificate for the 3-connectedness of graphs that can be easily computed and verified.
منابع مشابه
Certifying 3-Connectivity in Linear Time
One of the most noted construction methods of 3-vertex-connected graphs is due to Tutte and based on the following fact: Every 3-vertexconnected graph G on more than 4 vertices contains a contractible edge, i. e., an edge whose contraction generates a 3-connected graph. This implies the existence of a sequence of edge contractions from G to K4 such that every intermediate graph is 3-vertex-conn...
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