Sebastian M. Cioabă

Matchings in regular graphs from eigenvalues

Let G be a connected k-regular graph of order n. We find a best upper bound (in terms of k) on the third largest eigenvalue that is sufficient to guarantee that G has a perfect matching when n is even, and a matching of order n-1 when n is odd. We also examine how other eigenvalues affect the size of matchings in G.

Edge-Connectivity, Eigenvalues, and Matchings in Regular Graphs

In this paper, we study the relationship between eigenvalues and the existence of certain subgraphs in regular graphs. We give a condition on an appropriate eigenvalue that guarantees a lower bound for the matching number of a

On the spectrum of Wenger graphs

t

Variations on a theme of Graham and Pollak

-edge-connected

On decompositions of complete hypergraphs

d

Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs

-regular graph when

Some Applications of Eigenvalues of Graphs

t\leq d-2

Expander graphs and gaps between primes

. This work extends some classical results of von Baebler [Comment. Math. Helv., 10 (1937), pp. 275-287] and Berge [Theorie des Graphes et Ses Applications, Collection Universitaire de Mathematiques II, Dunod, Paris, 1958] and more recent work of Cioaba, Gregory, and Haemers [J. Combin. Theory Ser. B, 99 (2009), pp. 287-297]. We also study the relationships between the eigenvalues of a

Max-cut and extendability of matchings in distance-regular graphs

d

Maximizing the Order of a Regular Graph of Given Valency and Second Eigenvalue

-regular