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On The p-Schatten Energy Of Bipartite Graphs
We give a Coulson integral formula and a Coulson-Jacobs formula for the p -Schatten energy of bipartite graphs. We use these formulas to compare the p -...
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Steiner Subratio of Riemannian Manifolds
The Steiner subratio is one of the Steiner-type ratios that show how much the weights of optimal connecting graphs in a metric space can differ. In...
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Constructing Tree-Decompositions That Display All Topological Ends
We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.
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A lower bound for the 3-pendant tree-connectivity of lexicographic product graphs
for a connected graph G = ( V, E ) and a set S ⊆ V ( G ) with at least two vertices, an S -Steiner tree is a subgraph T = ( V ′, E ′) of G that is a tree with S ...
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The relation between the number of leaves of a tree and its diameter
Let L ( n, d ) denote the minimum possible number of leaves in a tree of order n and diameter d . Lesniak (1975) gave the lower bound B ( n,d ) = ⌈2( n − 1)/ d ...
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The Number of Subuniverses, Congruences, Weak Congruences of Semilattices Defined by Trees
We determine the number of subuniverses of semilattices defined by arbitrary and special kinds of trees via combinatorial considerations. Using a...
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Poincaré inequalities on graphs
Every graph of bounded degree endowed with the counting measure satisfies a local version of L p -Poincaré inequality, p ∈ [1, ∞]. We show that on...
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Big Ramsey Degrees of 3-Uniform Hypergraphs Are Finite
We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known...
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Spanning trees whose reducible stems have a few branch vertices
Let T be a tree. Then a vertex of T with degree one is a leaf of T and a vertex of degree at least three is a branch vertex of T . The set of leaves...
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An Area Theorem for Joint Harmonic Functions on the Product of Homogeneous Trees
For harmonic functions v on the disc, it has been known for a long time that non-tangential boundedness a.e.is equivalent to finiteness a.e. of the...
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Wiener index of graphs with fixed number of pendant or cut-vertices
The Wiener index of a connected graph is defined as the sum of the distances between all unordered pairs of its vertices. We characterize the graphs...
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Spectrum of Gallai Graph of Some Graphs
The Gallai graph Γ( G ) of a graph G , has the edges of G as its vertices and two distinct vertices are adjacent in Γ( G ) if they are adjacent edges in G ,...
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Packing four copies of a tree into a complete bipartite graph
In considering packing three copies of a tree into a complete bipartite graph, H. Wang (2009) gives a conjecture: For each tree T of order n and each...
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The Minimum Stretch Spanning Tree Problem for Typical Graphs
With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the...
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Weighted composition operators on discrete weighted Banach spaces
We study weighted composition operators on weighted Banach spaces over unbounded, locally finite metric spaces. We characterize the operators that...