Resource relocation on asymmetric networks.
Restrained domination in unicyclic graphs
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S. The restrained domination number of G, denoted by , is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then , and provide a characterization of graphs achieving this bound.
Restricted 123-involutions.
Restricted and quasi-toral restricted Lie-Rinehart algebras
In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be....
Restricted Eulerian circuits in directed graphs
Restricted partitions and q-Pell numbers
In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p...
Restricted permutations and Chebyshev polynomials.
Restricted permutations, continued fractions, and Chebyshev polynomials.
Restricted permutations, Fibonacci numbers, and -generalized Fibonacci numbers.
Restricted permutations from Catalan to Fine and back.
Restricted set addition in groups. II: A generalization of the Erdős-Heilbronn conjecture.
Restricted sumsets in finite vector spaces: the case .
Restricted walks in regular trees.
Restricting supercharacters of the finite group of unipotent uppertriangular matrices.
Results on -continuous graphs
For any nontrivial connected graph and any graph , the -degree of a vertex in is the number of copies of in containing . is called -continuous if and only if the -degrees of any two adjacent vertices in differ by at most 1; is -regular if the -degrees of all vertices in are the same. This paper classifies all -continuous graphs with girth greater than 3. We show that for any nontrivial connected graph other than the star , , there exists a regular graph that is not...
Reverse mathematics of some topics from algorithmic graph theory
This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.
Revisiting two classical results on graph spectra.
Reziprozitätsgesetze in der kombinatorischen Zähltheorie.
Rhombus tilings of a hexagon with two triangles missing on the symmetry axis.
Ribbon tableaux, Hall-Littlewood functions and unipotent varieties.