Obstructions for partitioning into forests and outerplanar graphs

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For a class C of graphs, we define C-edge-brittleness of a graph G as the minimum ℓ such that the vertex set of G can be partitioned into sets inducing a subgraph in C and there are ℓ edges having ends in distinct parts. We characterize classes of graphs having bounded C-edge-brittleness for a class C of forests or a class C of graphs with no K4∖e topological minors in terms of forbidden obstructions. We also define C-vertex-brittleness of a graph G as the minimum ℓ such that the edge set of G can be partitioned into sets inducing a subgraph in C and there are ℓ vertices incident with edges in distinct parts. We characterize classes of graphs having bounded C-vertex-brittleness for a class C of forests or a class C of outerplanar graphs in terms of forbidden obstructions. We also investigate the relations between the new parameters and the edit distance. © 2020 The Author(s)
Publisher
ELSEVIER
Issue Date
2022-05
Language
English
Article Type
Article
Citation

DISCRETE APPLIED MATHEMATICS, v.312, pp.15 - 28

ISSN
0166-218X
DOI
10.1016/j.dam.2020.09.006
URI
http://hdl.handle.net/10203/292543
Appears in Collection
MA-Journal Papers(저널논문)
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