Rainbow meanders and Cartesian billiards

Rainbow meanders and Cartesian billiards

In this paper we relate several objects from quite diverse areas of mathematics. Closed meanders are the configurations which arise when one or several disjoint closed Jordan curves in the plane intersect the horizontal axis transversely. The question of their connectivity also arises when evaluating traces in Temperley-Lieb algebras. The variant of open meanders is closely related to the detai...

On the rainbow connection of Cartesian products and their subgraphs

Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above by the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rain...

On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles

‎Let G be a graph‎. ‎A 2-rainbow dominating function (or‎ 2-RDF) of G is a function f from V(G)‎ ‎to the set of all subsets of the set {1,2}‎ ‎such that for a vertex v ∈ V (G) with f(v) = ∅, ‎the‎‎condition $bigcup_{uin N_{G}(v)}f(u)={1,2}$ is fulfilled‎, wher NG(v)  is the open neighborhood‎‎of v‎. ‎The weight of 2-RDF f of G is the value‎‎$omega (f):=sum _{vin V(G)}|f(v)|$‎. ‎The 2-rainbow‎‎d...

River Restoration and Meanders

Among the most visually striking river restoration projects are those that involve the creation of a new channel, often in a new alignment and generally with a form and dimensions that are different from those of the preproject channel. These channel reconstruction projects often have the objective of creating a stable, single-thread, meandering channel, even on rivers that were not historicall...

Meanders and Motzkin Words