5 research outputs found
A Survey of Best Monotone Degree Conditions for Graph Properties
We survey sufficient degree conditions, for a variety of graph properties,
that are best possible in the same sense that Chvatal's well-known degree
condition for hamiltonicity is best possible.Comment: 25 page
Best monotone degree conditions for binding number
AbstractWe give sufficient conditions on the vertex degrees of a graph G to guarantee that G has binding number at least b, for any given b>0. Our conditions are best possible in exactly the same way that Chvátal’s well-known degree condition to guarantee a graph is Hamiltonian is best possible
Signless Laplacian spectral radius for a k-extendable graph
Let and be two nonnegative integers with (mod 2), and let
be a graph of order with a 1-factor. Then is said to be
-extendable for if every matching in of size
can be extended to a 1-factor. In this paper, we first establish a lower
bound on the signless Laplacian spectral radius of to ensure that is
-extendable. Then we create some extremal graphs to claim that all the
bounds derived in this article are sharp.Comment: 11 page
Matching extension and distance spectral radius
A graph is called k-extendable if each k-matching can be extended to a perfect matching. We give spectral conditions for the k-extendability of graphs and bipartite graphs using Tutte-type and Hall-type structural characterizations. Concretely, we give a sufficient condition in terms of the spectral radius of the distance matrix for the k-extendability of a graph and completely characterize the corresponding extremal graphs. A similar result is obtained for bipartite graphs.</p