General results on the enumeration of strings in Dyck paths.
General symmetric starter of orthogonal double covers of complete bipartite graph.
Généralisation d'identités de Carlitz, Howard et Lehmer.
Generalisation of a Number-Theoretical Result
Generalised irredundance in graphs: Nordhaus-Gaddum bounds
For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by . Only 64 Boolean functions f can produce different classes , special cases of which include...
Generalised Semiplanes and Certain Divisible Partial Designs.
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Generalization of one Baer's theorem for nets
Generalization of two identities in Ramanujan's lost notebook
Generalization of Waring-type formulas. (Généralisation de formules de type Waring.)
Generalization of Železník's theorem on embeddings of tensor products of graphs
Generalizations and refinements of a partition theorem of Göllnitz.
Generalizations Of A Reccurence Relation For The Characteristic Polynomials Of Trees
Generalizations of Carlitz compositions.
Generalizations of Cole's Systems
There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.
Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.
Generalizations of partial difference sets from cyclotomy to nonelementary Abelian -groups.
Generalizations of Schur's partition theorem.
Generalizations of the tree packing conjecture
The Gyárfás tree packing conjecture asserts that any set of trees with 2,3,...,k vertices has an (edge-disjoint) packing into the complete graph on k vertices. Gyárfás and Lehel proved that the conjecture holds in some special cases. We address the problem of packing trees into k-chromatic graphs. In particular, we prove that if all but three of the trees are stars then they have a packing into any k-chromatic graph. We also consider several other generalizations of the conjecture.
Generalized 3-edge-connectivity of Cartesian product graphs
The generalized -connectivity of a graph was introduced by Chartrand et al. in 1984. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized -edge-connectivity which is defined as and , where denotes the maximum number of pairwise edge-disjoint trees in such that for . In this paper we prove that for any two connected graphs and we have , where is the Cartesian product of and . Moreover, the bound is sharp. We also obtain the...