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Combined degree and connectivity conditions for H-linked graphs
Combined degree connectivity conditions H-linked graphs Combinatorics
2012/6/27
For a given multigraph H, a graph G is H-linked, if |G| \geq |H| and for every injective map {\tau}: V (H) \rightarrow V (G), we can find internally disjoint paths in G, such that every edge from uv i...
This note deals with the relationship between the total number of $k$-walks in a graph, and the sum of the $k$-th powers of its vertex degrees. In particular, it is shown that the the number of all $k...
Counting independent sets of a fixed size in graphs with a given minimum degree
graphs given minimum degree independent sets Combinatorics
2012/4/16
Galvin showed that for all fixed $\delta$ and sufficiently large $n$, the $n$-vertex graph with minimum degree $\delta$ that admits the most independent sets is the complete bipartite graph $K_{\delta...
Maximum spectral radius of graphs with given connectivity and minimum degree
connectivity spectral radius Combinatorics
2011/9/21
Abstract: Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most $k$, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order $n$ with $\kappa(G) \...
On a Greedy 2-Matching Algorithm and Hamilton Cycles in Random Graphs with Minimum Degree at Least Three
Greedy 2-Matching Algorithm Hamilton Cycles Random Graphs Minimum Degree
2011/9/20
Abstract: We describe and analyse a simple greedy algorithm \2G\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\d\geq 3}$ when $c\geq 15$. A 2-matching is a spanning subgraph of ma...
On a sparse random graph with minimum degree {three}: Likely Posa's sets are large
random sparse graphs degrees longest path Posa sets
2011/9/20
Abstract: We consider the likely size of the endpoint sets produced by Posa rotations, when applied to a longest path in a random graph with $cn,\,c\geq 2.7$ edges that is conditioned to have minimum ...
Reverse degree distance of unicyclic graphs
Degree Distance Reverse degree distance Diameter Unicyclic graph Pendant vertices Maximum degree
2011/9/1
Abstract: The reverse degree distance is a connected graph invariant closely related to the degree distance proposed in mathematical chemistry. We determine the unicyclic graphs of given girth, number...
Abstract: The degree chromatic polynomial $Pm(G,k)$ of a graph $G$ counts the number of $k$-colorings in which no vertex has $m$ adjacent vertices of its same color. We prove Humpert and Martin's conj...
Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes
secant variety catalecticant minors Veronese variety Veronese reembeddings
2011/2/21
We study the secant varieties of the Veronese varieties and of Veronese reembeddings of a smooth projective variety.