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A chain theorem for sequentially 3-rank-connected graphs with respect to vertex-minors

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Title
A chain theorem for sequentially 3-rank-connected graphs with respect to vertex-minors
Author(s)
Duksang Lee; Sang-il Oum
Publication Date
2023-10
Journal
European Journal of Combinatorics, v.113
Publisher
Academic Press
Abstract
Tutte (1961) proved the chain theorem for simple 3-connected graphs with respect to minors, which states that every simple 3-connected graph G has a simple 3-connected minor with one edge fewer than G, unless G is a wheel graph. Bouchet (1987) proved an analog for prime graphs with respect to vertex-minors. We present a chain theorem for higher connectivity with respect to vertex-minors, showing that every sequentially 3-rank-connected graph G has a sequentially 3-rank-connected vertex-minor with one vertex fewer than G, unless |V(G)|≤12. © 2023 Elsevier Ltd
URI
https://pr.ibs.re.kr/handle/8788114/13875
DOI
10.1016/j.ejc.2023.103761
ISSN
0195-6698
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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