On random greedy triangle packing.
On recognition of strong graph bundles
On regular factors in regular graphs with small radius.
On resolving edge colorings in graphs.
On self-complementary cyclic packing of forests.
On some partitions of a graph, I
On star polynomials, graphical partitions and reconstruction.
On the balanced domination of graphs
Let be a graph and let denote the closed neighbourhood of a vertex in . A function is said to be a balanced dominating function (BDF) of if holds for each vertex . The balanced domination number of , denoted by , is defined as A graph is called -balanced if . The novel concept of balanced domination for graphs is introduced. Some upper bounds on the balanced domination number are established, in which one is the best possible bound and the rest are sharp, all the corresponding...
On the binding number of some Hallian graphs
On the completeness of decomposable properties of graphs
Let ₁,₂ be additive hereditary properties of graphs. A (₁,₂)-decomposition of a graph G is a partition of E(G) into sets E₁, E₂ such that induced subgraph has the property , i = 1,2. Let us define a property ₁⊕₂ by G: G has a (₁,₂)-decomposition. A property D is said to be decomposable if there exists nontrivial additive hereditary properties ₁, ₂ such that D = ₁⊕₂. In this paper we determine the completeness of some decomposable properties and we characterize the decomposable properties of completeness...
On the complexity of covering nodes by K node-disjoint cycles
On the decomposition of complete directed graphs into factors with given radii
On the Decomposition of the Complete Directed Graph into Factors with Given Diameters
On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges
Let Cm and Sm denote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, Kn, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where Kn is {Cm, Sm}-decomposable. We show that the obvious necessary condition is sufficient for such decompositions to exist for different values of m.
On the discrepancy of coloring finite sets.
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 Lexicographic and Costrong Product of Set Systems. (Über das lexikographische und das kostrake Produkt von Mengensystemen) (Short Communication)
On the number of 2-factors in rectangular lattice graphs.
On the number of dissimilar pfaffian orientations of graphs
On the number of dissimilar pfaffian orientations of graphs
A subgraph H of a graph G is conformal if G - V(H) has a perfect matching. An orientation D of G is Pfaffian if, for every conformal even circuit C, the number of edges of C whose directions in D agree with any prescribed sense of orientation of C is odd. A graph is Pfaffian if it has a Pfaffian orientation. Not every graph is Pfaffian. However, if G has a Pfaffian orientation D, then the determinant of the adjacency matrix of D is the square of the number of perfect matchings of G. (See the book...