SCATTERED CLASSES OF GRAPHSopen access
- Authors
- Kwon, O jung; Oum, Sang-Il
- Issue Date
- Mar-2020
- Publisher
- SIAM PUBLICATIONS
- Keywords
- graph structure; vertex-minor; subgraph
- Citation
- SIAM JOURNAL ON DISCRETE MATHEMATICS, v.34, no.1, pp.972 - 999
- Indexed
- SCIE
SCOPUS
- Journal Title
- SIAM JOURNAL ON DISCRETE MATHEMATICS
- Volume
- 34
- Number
- 1
- Start Page
- 972
- End Page
- 999
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/190701
- DOI
- 10.1137/19M1293776
- ISSN
- 0895-4801
- Abstract
- For a class C of graphs G equipped with functions f(G) defined on subsets of E(G) or V (G), we say that C is k-scattered with respect to f(G) if there exists a constant .e such that for every graph G is an element of C, the domain of f(G) can be partitioned into subsets of size at most k so that the union of every collection of the subsets has f(G) value at most We present structural characterizations of graph classes that are k-scattered with respect to several graph connectivity functions. In particular, our theorem for cut-rank functions provides a rough structural characterization of graphs having no mK(1,n) vertex-minor, which allows us to prove that such graphs have bounded linear rank-width.
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