Obstructions for partitioning into forests and outerplanar graphs

초록

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 K-4 \ 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. (C) 2020 The Author(s). Published by Elsevier B.V.

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