Regularly Derived Planes.
Regularly spaced subsums of integer partitions
Regulated buildups of 3-configurations
We deal with two types of buildups of 3-configurations: a generating buildup over a given edge set and a regulated one (according to maximal relative degrees of vertices over a penetrable set of vertices). Then we take account to minimal generating edge sets, i.e., to edge bases. We also deduce the fundamental relation between the numbers of all vertices, of all edges from edge basis and of all terminal elements. The topic is parallel to a certain part of Belousov' “Configurations in algebraic...
Relating different cycle spaces of the same infinite graph.
Relational quotients
Let 𝒦 be a class of finite relational structures. We define ℰ𝒦 to be the class of finite relational structures A such that A/E ∈ 𝒦, where E is an equivalence relation defined on the structure A. Adding arbitrary linear orderings to structures from ℰ𝒦, we get the class 𝒪ℰ𝒦. If we add linear orderings to structures from ℰ𝒦 such that each E-equivalence class is an interval then we get the class 𝒞ℰ[𝒦*]. We provide a list of Fraïssé classes among ℰ𝒦, 𝒪ℰ𝒦 and 𝒞ℰ[𝒦*]. In addition, we classify...
Relations between Kirchhoff index and Laplacian–energy–like invariant
Relations between the domination parameters and the chromatic index of a graph
In this paper we show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality...
Relations between -regular sets and star complements
Let be a finite graph with an eigenvalue of multiplicity . A set of vertices in is called a star set for in if is not an eigenvalue of the star complement which is the subgraph of induced by vertices not in . A vertex subset of a graph is -regular if it induces a -regular subgraph and every vertex not in the subset has neighbors in it. We investigate the graphs having a -regular set which induces a star complement for some eigenvalue. A survey of known results is provided...
Relations binaires entre partitions
Relations, coverings, hypergraphs and matroids
Relationships between conbinatorics and 0-simple semigroups.
Relationships between distance domination parameters.
Relative expressiveness of the edge/adjacency language for graph theory
Relativnullen und reduzible Mengen bei Differenzen von Mengen ganzer Zahlen.
Relaxations of Ore's condition on cycles.
Relaxed graceful labellings of trees.
Reliability of communication networks with delay constraints: computational complexity and complete topologies.
Remark about a construction of some tournaments points of certain projective planes
Remark on a paper of Lovász
Remark on inequalities for the Laplacian spread of graphs
Two inequalities for the Laplacian spread of graphs are proved in this note. These inequalities are reverse to those obtained by Z. You, B. Liu: The Laplacian spread of graphs, Czech. Math. J. 62 (2012), 155–168.