DNA recombination through assembly graphs Original Research Article

Motivated by DNA rearrangements and DNA homologous recombination modeled in [A. Angeleska, N. Jonoska, M. Saito, L.F. Landweber, RNA-guided DNA assembly, Journal of Theoretical Biology, 248(4) (2007), 706–720], we investigate smoothings on graphs that consist of only 4-valent and 1-valent rigid vertices, called assembly graphs. An assembly graph can be seen as a representation of the DNA during certain recombination processes in which 4-valent vertices correspond to the alignment of the recombination sites. A single gene is modeled by a polygonal path in an assembly graph. A polygonal path makes a “right-angle” turn at every vertex, defining smoothings at the 4-valent vertices and therefore modeling the recombination process. We investigate the minimal number of polygonal paths visiting all vertices of a given graph exactly once, and show that for every po