In this paper we enumerate k-noncrossing RNA pseudoknot structures with given minimum arc-and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length ≥ 3, stack-length ≥ σ and in which there are at most k − 1 mutually crossing bonds, denoted by T [3] k,σ (n). In particular we prove that the numbers of 3, 4 and 5-noncrossing RNA structures with arc-length ≥ 3 and...

A digraph D = (V, A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V , i.e. a hamiltonian path. Given a tournament T , it is well known that it contains a directed hamiltonian path. In this paper, we develop the structure necessary for a tournament T to contain an arc xy that is not on any hamiltonian path. Using this structure, we give suff...

Given positive integers k m n, a graphG of order n is ðk;mÞ-pancyclic if for any set of k vertices of G and any integer r with m r n, there is a cycle of length r containing the k vertices. Minimum degree conditions and minimum sum of degree conditions of nonadjacent vertices that imply a graph is ðk;mÞ-pancylic are proved. If the additional property that the k vertices must appear on the cycle...

The (n, k)-star graph is a generalized version of the n-star graph, which belongs to the class of Cayley graphs, and has been recognized as an attractive alternative to an n-cube for building massively parallel computers. Recently, Chen et al. showed that an (n, k)-star graph is 6-weak-vertex-pancyclic for k < n–1, that is, each vertex of an (n, k)-star graph is contained in a cycle of length r...

Background. The problem of atopic march (AM), namely its progression from monoorganic phenotypes dermatitis (AD), allergic rhinitis/rhinoconjunctivitis (AR/ARC), bronchial asthma (BA) to their multiorgan combinations, is one the biggest in modern pediatrics. One most important causes for development these pathologies are single nucleotide variants (SNV) causative genes, orsomucoid-1-like protei...

Agraph of order n is said to be pancyclic if it contains cycles of all lengths from three to n. Let G be a Hamiltonian graph and let x and y be vertices of G that are consecutive on some Hamiltonian cycle in G. Hakimi and Schmeichel showed (J Combin Theory Ser B 45:99–107, 1988) that if d(x) + d(y) ≥ n then either G is pancyclic, G has cycles of all lengths except n − 1 or G is isomorphic to a ...

Normal human peripheral blood contains a population of T cells (autologous reactive cells [ARC]) capable of proliferating in response to signals from autologous B cells and monocytes. Selective suicide of proliferating ARC with 5-bromo-2-deoxyuridine and light demonstrated that this ARC was responsive to signals coded for by genes more closely linked to the HLA-DR, than to the HLA-A, or HLA-B, ...

We characterize all pairs of connected graphs {X,Y } such that each 3-connected {X,Y }-free graph is pancyclic. In particular, we show that if each of the graphs in such a pair {X,Y } has at least four vertices, then one of them is the claw K1,3, while the other is a subgraph of one of six specified graphs.

The existence of a primitive element of GF (q) with certain properties is used to prove that all cycles that could theoretically be embedded in AG(2, q) and PG(2, q) can, in fact, be embedded there (i.e. these planes are ‘pancyclic’). We also study embeddings of wheel and gear graphs in arbitrary projective planes.