Graphs of bounded depth-2 rank-brittlenessopen access
- Authors
- Kwon, O jung; Oum, Sang-il
- Issue Date
- Mar-2021
- Publisher
- WILEY
- Keywords
- depth-r; rank-brittleness; pathrank-depth; vertex-minor
- Citation
- JOURNAL OF GRAPH THEORY, v.96, no.3, pp.361 - 378
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF GRAPH THEORY
- Volume
- 96
- Number
- 3
- Start Page
- 361
- End Page
- 378
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189702
- DOI
- 10.1002/jgt.22619
- ISSN
- 0364-9024
- Abstract
- 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.
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