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- W1997533166 abstract "In a recent work of Ayaka Shimizu, she studied an operation named region crossing change on link diagrams, which was proposed by Kishimoto, and showed that a region crossing change is an unknotting operation for knot diagrams. In this paper, we prove that the region crossing change on a 2-component link diagram is an unknotting operation if and only if the linking number of the diagram is even. Besides, we define an incidence matrix of a link diagram via its signed planar graph and its dual graph. By studying the relation between region crossing change and incidence matrix, we prove that a signed planar graph represents an n-component link diagram if and only if the rank of the associated incidence matrix equals c − n + 1, where c denotes the size of the graph." @default.
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- W1997533166 date "2012-05-23" @default.
- W1997533166 modified "2023-10-16" @default.
- W1997533166 title "On region crossing change and incidence matrix" @default.
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- W1997533166 doi "https://doi.org/10.1007/s11425-012-4403-1" @default.
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