Finding shortest contractible and shortest separating cycles in embedded graphs

We give a polynomial-time algorithm to find a shortest contractible cycle (i.e. a closed walk without repeated vertices) in a graph embedded in a surface. This answers a question posed by Hutchinson. In contrast, we show that finding a shortest contractible cycle through a given vertex is NP-hard. We also show that finding a shortest separating cycle in an embedded graph is NP-hard. This answers a question posed by Mohar and Thomassen.

• Type: Journal
• Year: 2010
• Where: TALG
• Authors: Sergio Cabello
• Keywords: Natural Language Processing, NP-hard, Shortest Contractible Cycle, Shortest Separating Cycle, TALG 2010