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 $\Gamma$ 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 $\Gamma$, 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.
@article{10_37236_13360,
author = {Bo\v{s}tjan Kuzman and Primo\v{z} \v{S}parl},
title = {On the fractional matching extendability of {Cayley} graphs of abelian groups},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/13360},
zbl = {8097637},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13360/}
}
TY - JOUR
AU - Boštjan Kuzman
AU - Primož Šparl
TI - On the fractional matching extendability of Cayley graphs of abelian groups
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/13360/
DO - 10.37236/13360
ID - 10_37236_13360
ER -
%0 Journal Article
%A Boštjan Kuzman
%A Primož Šparl
%T On the fractional matching extendability of Cayley graphs of abelian groups
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/13360/
%R 10.37236/13360
%F 10_37236_13360
Boštjan Kuzman; Primož Šparl. On the fractional matching extendability of Cayley graphs of abelian groups. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13360
