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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 504, Pages 21–46 (Mi znsl7108)  
Transformations of assembly number for 4-regular graphs

A. E. Gutermanabc, E. M. Kreinescb, N. V. Ostroukhovab

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Lomonosov Moscow State University
c Moscow Center for Fundamental and Applied Mathematics
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Abstract: Simple assembly graphs characterize the process of DNA recombination in living cells. The assembly number, number of distinct Hamiltonian sets of polygonal paths, one-sided and middle additivity of a graph are important characteristics of such graphs. This paper investigates transformations of simple assembly graphs that allow one to increase the assembly number or to obtain middle additive graphs. Also the minimum number of loops that must be added to the edges of a tangled chord graph in order to increase its assembly number by 1 is computed.
Key words and phrases: assembly graphs, doubly occurrence words, assembly number.
Funding agency Grant number
Russian Science Foundation 17-11-01124
Received: 13.10.2021
Document Type: Article
UDC: 512.543+519.177
Language: Russian
Citation: A. E. Guterman, E. M. Kreines, N. V. Ostroukhova, “Transformations of assembly number for 4-regular graphs”, Computational methods and algorithms. Part XXXIV, Zap. Nauchn. Sem. POMI, 504, POMI, St. Petersburg, 2021, 21–46
Citation in format AMSBIB
\Bibitem{GutKreOst21}
\by A.~E.~Guterman, E.~M.~Kreines, N.~V.~Ostroukhova
\paper Transformations of assembly number for 4-regular graphs
\inbook Computational methods and algorithms. Part~XXXIV
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 504
\pages 21--46
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7108}
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