Fast Exponential-Time Algorithms to solve NP-complete ... - Lita

33/52Fast Exponential-Time AlgorithmsBranchingThe Algorithm of Fomin et al.Folding a vertex of degree twoSuppose v has degree two and its neighbors u 1 and u 2 arenon-adjacent. Folding the node v of G is the process oftransforming G into a new graph ˜G = ˜G(v) by :(1) adding a new node u 12 ;(2) adding edges between u 12 and the nodes in N(u 1 ) ∪ N(u 2 ) ;(3) removing N[v].Lemma (Folding)For any graph G and for any node v of G with degree two and twonon-adjacent neighbors :α(G) = 1 + α(˜G(v)).