A Šoltés’ hypergraph is a hypergraph for which the removal of any of its vertices does not change its total distance. We prove that every uniform Šoltés’ hypergraph has order at least 10, there exist uniform Šoltés’ hypergraphs for every order at least 10 and for almost every uniformity, and there exists a non-regular uniform Šoltés’ hypergraph. By also providing infinitely many weighted Šoltés’ graphs, we conclude that the Šoltés’ problem can be answered positively for most natural generalisations of graphs.

Rights

URN

URN:NBN:SI:doc-UACOT9X9

COBISSID

294231811

DOI

10.26493/1855-3974.3643.9f6

Added

27.10.2026

Metadata

Citation

APA:

Cambie, Stijn, Tiwari, Ajay (2026). Uniform Šoltés’ hypergraphs and Šoltés’ weighted graphs. Ars mathematica contemporanea, volume 26, issue 4, article p4.09, str. 1-12. URN:NBN:SI:doc-UACOT9X9 from http://www.dlib.si

MLA:

Cambie, Stijn, Tiwari, Ajay. "Uniform Šoltés’ hypergraphs and Šoltés’ weighted graphs." Ars mathematica contemporanea volume 26. issue 4. article p4.09 (2026) str. 1-12.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-UACOT9X9>