On the existence of 1-factors in partial squares of graphs
On the existence of a -factor in the fourth power of a graph
On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph
We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.
On the Existence of Certain Graphs with Diameter Two
On the existence of critically n-connected graphs
On the existence of graphs with a certain ordering of vertices
On the Existence of (k,l)-Kernels in Infinite Digraphs: A Survey
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction was done for...
On the expectation and variance of the reversal distance.
On the exponent of -regular primitive matrices.
On the Extension of Graphs with a Given Diameter without Superfluous Edges
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 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 function “sandwiched" between and .
On the functions with values in .
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 Graph for which there is a Tree as the Inverse Interchange Graph of a Local Graph.