Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Seminar of Graph Theory - Štefko Miklavič (10.11.2016)

Thursday 10.11.2016 at 9:50, Lecture room M/213

07. 11. 2016 09.43 hod.
By: Robert Jajcay

Štefko Miklavič (University of Primorska, Koper):
Matching extendability of Deza graphs

Let $\Gamma$ be a connected graph. A matching $M$ of $\Gamma$ is a set of pairwise non-adjacent edges; that is, no two edges share a common vertex. A vertex of $\Gamma$ is matched by a matching $M$ if it is an endpoint of one of the edges in $M$. A perfect matching of $\Gamma$ is a matching which matches all vertices of $\Gamma$. Graph $\Gamma$ of even order is $n$-extendable, if

(i) it contains a matching of size $n$ and
(ii) every such matching is contained in a perfect matching of $\Gamma$.


In this talk we will review known results about extendability of strongly regular graphs, distance-regular graphs and Deza graphs.