Extremal edge general position sets in some graphs

Tian, Jing (author), Klavžar, Sandi (author), Tan, Elif (author)

A set of edges $X\subseteq E(G)$ of a graph $G$ is an edge general position set if no three edges from $X$ lie on a common shortest path. The edge general position number ${\rm gp}_{\rm e}(G)$ of $G$ is the cardinality of a largest edge general position set in $G$. Graphs $G$ with ${\rm gp}_{\rm e}(G) = |E(G)| - 1$ and with ${\rm gp}_{\rm e}(G) = 3$ are respectively characterized. Sharp upper and lower bounds on ${\rm gp}_{\rm e}(G)$ are proved for block graphs $G$ and exact values are determined for several specific block graphs.

• Language: English
• Keywords: general position set, edge general position set, cut-vertex, diametral path, block graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 11 str.
• Numbering: Vol. 40, iss. 2, art. 40
• PID: 20.500.12556/RUL-155353
• UDC: 519.17
• ISSN on article: 0911-0119
• DOI: 10.1007/s00373-024-02770-z
• COBISS.SI-ID: 190484739
• Publication date in RUL: 27.03.2024

Record is a part of a journal

• Title: Graphs and combinatorics
• Shortened title: Graphs comb.
• Publisher: Springer Nature
• ISSN: 0911-0119
• COBISS.SI-ID: 25536512

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: množica v splošni legi, množica povezav v splošni legi, prerezno vozlišče, premerna pot, bločni grafi