A bijection between planar constellations and some colored Lagrangian trees.
A bound for the Steiner tree problem in graphs
A characterization of hypergraphs generated by arborescences
A characterization of roman trees
A Roman dominating function (RDF) on a graph G = (V,E) is a function f: V → 0,1,2 satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of f is . The Roman domination number is the minimum weight of an RDF in G. It is known that for every graph G, the Roman domination number of G is bounded above by twice its domination number. Graphs which have Roman domination number equal to twice their domination number are called...
A classification of separable Rosenthal compacta and its applications [Book]
A combinatorial derivation of the number of labeled forests.
A combinatorial proof of Postnikov's identity and a generalized enumeration of labeled trees.
A combinatorial ranking problem.
A combinatorial ranking problem. (Short Communication).
A Décomposition Theorem on Euclidean Steiner Minimal Trees.
A distance between isomorphism classes of trees
A few remarks on the history of MST-problem
On the background of Borůvka’s pioneering work we present a survey of the development related to the Minimum Spanning Tree Problem. We also complement the historical paper Graham-Hell [GH] by a few remarks and provide an update of the extensive literature devoted to this problem.
A formula for all minors of the adjacency matrix and an application
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.
A generalization of Hamiltonian cycles for trees
A Generalization of the Matrix-Tree Theorem.
A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs
A Link Between Ordered Sets And Trees On The Rectangle Tree Hypothesis
A lower bound for the irredundance number of trees
Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result. ...
A modification of the median of a tree
The concept of median of a tree is modified, considering only distances from the terminal vertices instead of distances from all vertices.
A multivariate Lagrange inversion formula for asymptotic calculations.