On the Problems of CF -Connected Graphs for K l,m,n

Michal Staš () and Mária Timková
Additional contact information
Michal Staš: Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia
Mária Timková: Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, 042 00 Košice, Slovakia

Mathematics, 2024, vol. 12, issue 13, 1-18

Abstract: A connected graph, G , is Crossing Free -connected ( CF -connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G . We conjecture that a complete tripartite graph, K l , m , n , is CF -connected if and only if it does not contain any of the following as a subgraph: K 1 , 2 , 7 , K 1 , 3 , 5 , K 1 , 4 , 4 , K 2 , 2 , 5 , K 3 , 3 , 3 . We examine the idea that K 1 , 2 , 7 , K 1 , 3 , 5 , K 1 , 4 , 4 , and K 2 , 2 , 5 are the first non- CF -connected complete tripartite graphs. The CF -connectedness of K l , m , n with l , m , n ≥ 3 is dependent on the knowledge of crossing numbers of K 3 , 3 , n . In this paper, we prove various results that support this conjecture.

Keywords: crossing number; crossing sequence; connectivity; complete tripartite graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/13/2068/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/13/2068/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:13:p:2068-:d:1427071

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().