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Graphs of bounded depth-2 rank-brittleness

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Title
Graphs of bounded depth-2 rank-brittleness
Author(s)
O-joung Kwon; Sang-il Oum
Publication Date
2021-03
Journal
JOURNAL OF GRAPH THEORY, v.96, no.3, pp.361 - 378
Publisher
WILEY
Abstract
@WILEY We characterize classes of graphs closed under taking vertex-minors and having noPnand no disjoint union ofncopies of the 1-subdivision ofK1,nfor somen. Our characterization is described in terms of a tree of radius 2 whose leaves are labeled by the vertices of a graphG, and the width is measured by the maximum possible cut-rank of a partition ofV(G)induced by splitting an internal node of the tree to make two components. The minimum width possible is called the depth-2 rank-brittleness ofG. We prove that for alln, every graph with sufficiently large depth-2 rank-brittleness containsPnor disjoint union ofncopies of the 1-subdivision ofK1,nas a vertex-minor
URI
https://pr.ibs.re.kr/handle/8788114/10039
DOI
10.1002/jgt.22619
ISSN
0364-9024
Appears in Collections:
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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