Work

Mutual-visibility problems in Kneser and Johnson graphs

Year: 2024

Type: article

Abstract: Let G be a connected graph and X ⊆ V(G). By definition, two vertices u and v are X-visible in G if there exists a shortest u, v-path with all internal vertices being outside of the set X. The largest size of X such that any two vertices of G (resp. any two vertices from X) are X-visible is the total mutual-visibility number (resp. the mutual-visibility number) of G. In this paper, we determine the total mutual-visibility number of Kneser graphs, bipartite Kneser graphs, and Johnson graphs. The formulas proved for Kneser, and bipartite Kneser graphs are related to the size of transversal-critical uniform hypergraphs, while the total mutual-visibility number of Johnson graphs is equal to a hypergraph Turán number. Exact values or estimations for the mutual-visibility number over these graph classes are also established.

Source: Ars Mathematica Contemporanea

DOI: 10.26493/1855-3974.3344.4c8

Authors: Gülnaz Boruzanlı Ekinci, Csilla Bujtás

Institutions: Ege University, University of Pannonia, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: Ege Üniversitesi

OpenAlex ID: W4403220234

FWCI: 0.975

Cites:

Cited by: 5

Related to: 10