On the Extension of Graphs with a Given Diameter without Superfluous Edges
On the - and -triangle of the barycentric subdivision of a simplicial complex
For a simplicial complex we study the behavior of its - and -triangle under the action of barycentric subdivision. In particular we describe the - and -triangle of its barycentric subdivision . The same has been done for - and -vector of by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the -triangle of are nonnegative, then the entries of the -triangle of are also nonnegative. We conclude with a few properties of the -triangle of .
On the factorization of reducible properties of graphs into irreducible factors
A hereditary property R of graphs is said to be reducible if there exist hereditary properties P₁,P₂ such that G ∈ R if and only if the set of vertices of G can be partitioned into V(G) = V₁∪V₂ so that ⟨V₁⟩ ∈ P₁ and ⟨V₂⟩ ∈ P₂. The problem of the factorization of reducible properties into irreducible factors is investigated.
On the failing cases of the Johnson bound for error-correcting codes.
On the first eigenvalue of bipartite graphs.
On the forcing geodetic and forcing steiner numbers of a graph
For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W-tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steiner set containing T. A forcing subset for W of minimum cardinality is a minimum forcing subset of W. The...
On the formal inverse of polynomial endomorphisms
On the formula of Goulden and Rattan for Kerov polynomials.
On the Fourier transform on the infinite symmetric group.
On the function “sandwiched" between and .
On the functions with values in .
On the Fundamental Group of self-affine plane Tiles
Let be an expanding matrix, a set with elements and define via the set equation . If the two-dimensional Lebesgue measure of is positive we call a self-affine plane tile. In the present paper we are concerned with topological properties of . We show that the fundamental group of is either trivial or uncountable and provide criteria for the triviality as well as the uncountability of . Furthermore, we give a short proof of the fact that the closure of each component of is a locally...
On the General Motion-Planning Problem with Two Degrees of Freedom.
On the generation and enumeration of some classes of convex polyominoes.
On the genus distribution of -dipoles.
On the genus of the complex projective plane.
On the genus of the graph of tilting modules.
On the Geometry and Combinatorics of the Array of Multinomial Coefficients
On the Graph for which there is a Tree as the Inverse Interchange Graph of a Local Graph.
On the Graph of Large Distances.