On the fractional matching extendability of Cayley graphs of abelian groups

Kuzman, Boštjan (author), Šparl, Primož (author)

Fractional matching extendability is a concept that brings together two widely studied topics in graph theory, namely that of fractional matchings and that of matching extendability. A fractional matching of a graph Γ with edge set E is a function f from E to the real interval [0,1] with the property that for each vertex v of Γ, the sum of f-values of all the edges incident to v is at most 1. When this sum equals 1 for each vertex v, the fractional matching is perfect. A graph of order at least 2t+1 is fractional t-extendable if it contains a matching of size t and if each such matching M can be extended to a fractional perfect matching in the sense that the corresponding function f assigns value 1 to each edge of M. In this paper, we study fractional matching extendability of Cayley graphs of Abelian groups. We show that, except for the odd cycles, all connected Cayley graphs of Abelian groups are fractional 1-extendable and we classify the fractional 2-extendable Cayley graphs of Abelian groups. This extends the classification of 2-extendable (in the classical sense) connected Cayley graphs of Abelian groups of even order from 1995, obtained by Chan, Chen and Yu.

• Language: English
• Keywords: fractional matching extendability, Cayley graph, abelian groups
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 22 str.
• Numbering: Vol. 32, iss. 3, art. P3.9
• PID: 20.500.12556/RUL-170844
• UDC: 519.17
• ISSN on article: 1077-8926
• DOI: 10.37236/13360
• COBISS.SI-ID: 242972931
• Publication date in RUL: 18.07.2025

Record is a part of a journal

• Title: The Electronic journal of combinatorics
• Shortened title: Electron. j. comb.
• Publisher: N.J. Calkin and H.S. Wilf
• ISSN: 1077-8926
• COBISS.SI-ID: 6973785

Licences

• License: CC BY-ND 4.0, Creative Commons Attribution-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nd/4.0/
• Description: Under the NoDerivatives Creative Commons license one can take a work released under this license and re-distribute it, but it cannot be shared with others in adapted form, and credit must be provided to the author.

Secondary language

• Language: Slovenian
• Keywords: Abelove skupine, Cayleyjev graf