Genus Ranges of 4-Regular Rigid Vertex GraphsReport as inadecuate



 Genus Ranges of 4-Regular Rigid Vertex Graphs


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We introduce a notion of genus range as a set of values of genera over all surfaces into which a graph is embedded cellularly, and we study the genus ranges of a special family of four-regular graphs with rigid vertices that has been used in modeling homologous DNA recombination. We show that the genus ranges are sets of consecutive integers. For any positive integer $n$, there are graphs with $2n $ vertices that have genus range ${m,m+1,

.,m}$ for all $0\le m



Author: Dorothy Buck; Egor Dolzhenko; Natasha Jonoska; Masahico Saito; Karin Valencia

Source: https://archive.org/







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