In the definition of the graph parameters μ(G) and ν(G), introduced by Colin de Verdière, and in the definition of the graph parameter ξ(G), introduced by Barioli, Fallat, and Hogben, a transversality condition is used, called the Strong Arnol’d Hypothesis. In this paper, we define the Strong Arnol’d Hypothesis for linear subspaces L ⊆ R with respect to a graph G = (V,E), with V = {1, 2, . . . ...

We give sufficient conditions for a tripartite graph to have a spanning subgraph consisting of complete graphs of order 3. This is applied to bound the strong chromatic number of a graph.

established definitions and theory), focuses on focuses on participants’ perspectives, and describes the results using expressive and persuasive language (Creswell, 1998). Qualitative research has some distinct characteristics (Flick et al, 2004), including: there is no single all-encompassing method, but a spectrum of methods from which one can be chosen depending on the research question it h...

In this work, we present a practical passive attack on SASI, an ultra-lightweight mutual authentication protocol for RFID. This attack can be used to reveal with overwhelming probability the secret ID of the prover by eavesdropping about 2 authentications. The result dismantles SASI and, more generally, provides a new approach that threatens ultra-lightweight authentication protocols.

In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. Also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.