Журнал Белорусского государственного университета: Математика, информатика | |
Graphs of intersections of closed polygonal chains | |
Ekaterina N. Dul1  Nikolai P. Prochorov1  | |
[1] Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus; | |
关键词: intersection graph; intersection graph of closed polygonal chains; regular graph; np-completeness; polynomial-time reduction; | |
DOI : 10.33581/2520-6508-2021-1-54-68 | |
来源: DOAJ |
【 摘 要 】
In the paper such subclass of string graphs as intersection graphs of closed polygonal chains (class of CPC-graphs) was considered, necessary conditions for belonging to that class, forbidden subgraphs and operations with graphs which preserve belonging to the CPC class were found. Considered question about the existence of k-regular CPC-graphs, particularly, pairs (k, n), such that there exists k-regular CPC-graph on n vertexes were found, proved that there are infinitely many k-regular CPC-graphs for any k ∈ N, estimations for the number of k, such that k-regular graph on n vertexes exists, were given. Algorithmic questions in the class of CPC-graphs were investigated. It was proved that independent and dominating set problems, coloring problem and the problem about maximal cycle are NP-hard in the class of CPC-graphs, and problem of recognition of the CPC-graphs belongs to the PSPACE class.
【 授权许可】
Unknown