Graphs of intersections of closed polygonal chains

Журнал Белорусского государственного университета: Математика, информатика

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