On a characterization of graphs by average labellings
The additive hereditary property of linear forests is characterized by the existence of average labellings.
On a characterization of -trees
A graph is a -tree if either is the complete graph on vertices, or has a vertex whose neighborhood is a clique of order and the graph obtained by removing from is also a -tree. Clearly, a -tree has at least vertices, and is a 1-tree (usual tree) if and only if it is a -connected graph and has no -minor. In this paper, motivated by some properties of 2-trees, we obtain a characterization of -trees as follows: if is a graph with at least vertices, then is a -tree if...
On a characterization of symmetric balanced incomplete block designs
All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number ofblocks bi and the expression Si for...
On a class of combinatorial Diophantine equations.
On a class of combinatorial sums involving generalized factorials.
On a class of commutative groupoids determined by their associativity triples
Let be a commutative groupoid such that ; ; or . Then is determined uniquely up to isomorphism and if it is finite, then for an integer .
On a class of distributive Steiner quasigroups
On a class of equations with special degrees over finite fields
On a class of partial -spreads of arising from scrolls.
On a class of polynomially solvable travelling salesman problems
On a class of polynomials associated with the cliques in a graph and its applications.
On a class of polynomials associated with the paths in a graph and its application to minimum nodes disjoint path coverings of graphs.
On a class of polynomials with integer coefficients.
On a Class of Vertex Folkman Numbers
Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3)...
On a classification of denumerable order types and an application to the partition calculus
On a classification of Hamiltonian tournaments
On a combinatorial problem of Asmus Schmidt.
On a combinatorical problem of K. Zarankiewicz
On a congruence for the number of finite marked topologies
On a conjecture by Nash-Williams