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Vertex-minors of graphs: A survey

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Title
Vertex-minors of graphs: A survey
Author(s)
Donggyu Kim; Sang-il Oum
Publication Date
2024-07
Journal
Discrete Applied Mathematics, v.351, pp.54 - 73
Publisher
Elsevier BV
Abstract
For a vertex v of a graph, the local complementation at v is an operation that replaces the neighborhood of v by its complement graph. Two graphs are locally equivalent if one is obtained from the other by a sequence of local complementations. A graph H is a vertex-minor of a graph G if H is an induced subgraph of a graph locally equivalent to G. Although this concept was introduced in the 1980s, it was not widely known and except for the survey paper of Bouchet published in 1990, there is no comprehensive survey listing all the new developments. We survey classic and recent theorems and conjectures on vertex-minors and related concepts such as circle graphs, cut-rank functions, rank-width, and interlace polynomials. © 2024 Elsevier B.V.
URI
https://pr.ibs.re.kr/handle/8788114/15111
DOI
10.1016/j.dam.2024.03.011
ISSN
0166-218X
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > 1. Journal Papers (저널논문)
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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