Assume we have two bijective functions U(x) and M(x) with M(x) 6= U(x) for all x and M,N : N → N . Every day and in different locations, we see the different results of U and M without seeing x. We are not assured about the time stamp nor the order within the day but at least the location is fully defined. We want to find the matching between U(x) and M(x) (i.e., we will not know x). We formula...

BASIC DEFINITIONS: crossing pair of curves and common interior point between two arcs. crossing number cr(G) minimum number of crossings in a drawing of G l-grid is a pair two disjoint edge subset E1, E2 ⊂ E of a drawing of a graph G = (V, E), such that |E1| = |E2| = l and every edge in E1 crosses every edge in E2 bi-clique complete bipartite graph where vertex classes differ in size by at most...

In this paper we show that, if G is a Berge graph such that neither G nor its complement G contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph (a bipartite graph, a line graph of a bipartite graph or the complement of such graphs) or it has a skew partition that cannot occur in a minimally imperfect graph. This structural result implie...

A claw-free graph G(V,E) is said to be basic if there exists a matching M ⊆ E whose edges are strongly bisimplicial and such that each connected component C of G − M is either a clique or a {claw, net}-free graph or satisfies α(G[C \ V (M)]) ≤ 3. The Maximum Weight Stable Set (MWSS) Problem in a basic claw-free graph can be easily solved by first solving at most four MWSS problems in each conne...

Molecular similarity is a pervasive concept in drug design. The basic idea underlying molecular similarity is the similar property principle, which states that structurally similar molecules will exhibit similar physicochemical and biological properties. In this paper, a new graph-based molecular descriptor (GBMD) is introduced. The GBMD is a new method of obtaining a rough description of 2D mo...

Compiler optimizations need precise and scalable analyses to discover program properties. We propose a partially flow-sensitive framework that tries to draw on the scalability of flow-insensitive algorithms while providing more precision at some specific program points. Provided with a set of critical nodes — basic blocks at which more precise information is desired — our partially flow-sensiti...

We study the stability number, chromatic number and clique cover of graphs with no induced P5 and diamonds. In particular, we provide a way to obtain all imperfect (P5, diamond)-free graphs by iterated point multiplication or substitution from a /nite collection of small basic graphs. Corollaries of this and other structural properties, among which a result of Bacs1 o and Tuza, are (i) combinat...

We propose a new layout paradigm for drawing a nested decomposition of a large network. The visualization supports the recognition of abstract features of the decomposition, while drawing all elements. In order to support the visual analysis that focuses on the dependencies of the individual parts of the decomposition, we use an annulus as the general underlying shape. This method has been eval...

Let G be a graph of order n and size m. A labeling of G is a bijective mapping θ : V(G) → {1, 2, . . . , n}, and we call Θ(G) the set of all labelings of G. For any graph G and any labeling θ ∈ Θ(G), let SL(G, θ) = ∑ e∈E(G)min{θ(u) : u ∈ e}. In this paper, we consider the S-Labeling problem, defined as follows: Given a graph G, find a labeling θ ∈ Θ(G) that minimizes SL(G, θ). The S-Labeling pr...

Multiple hop routing in mobile ad hoc networks can minimize energy consumption and increase data throughput. Yet, the problem of radio interferences remain. However if the routes are restricted to a basic network based on local neighborhoods, these interferences can be reduced such that standard routing algorithms can be applied. We compare different network topologies for these basic networks,...