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Sparse obstructions for minor-covering parameters.
- Source :
-
Discrete Applied Mathematics . May2020, Vol. 278, p28-50. 23p. - Publication Year :
- 2020
-
Abstract
- Given a finite set of graphs H and a non-negative integer k , we define A k (H) as the set containing every graph G that has k vertices whose removal provides a graph without any of the graphs in H as a minor. It is known that if H contains at least one planar graph then each obstruction in A k (H) has at most k c H vertices, for some c H depending only on the choice of H. In this paper, we investigate the size of the graphs in A k (H) that belong to certain classes of sparse graphs. In particular, we prove that for every graph F , if H contains at least one planar graph and only connected graphs, all graphs in A k (H) that are F -topological minor-free have at most c F , H ⋅ k vertices, where c F , H depends exclusively on the choice of H and F. Our result is a consequence of two more general conditions on graph parameters, namely the Finite Integer Index Property and Protrusion Decomposability, that can serve as a general framework for proving linear bounds for obstructions. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATROIDS
*PLANAR graphs
*SPARSE graphs
*GRAPH connectivity
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 278
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 142793253
- Full Text :
- https://doi.org/10.1016/j.dam.2019.10.021