We prove that perfect graphs with no balanced skew-partitions admits a O(n) Clique-Stable set separator. We then prove that for every graph G in this class, there always exists two subsets of vertices V1, V2 such that |V1|, |V2| ≥ c|V (G)| for some constant c and V1 is either complete or anticomplete to V2. The method uses trigraphs, introduced by Chudnovsky [5], and relies on the good behavior...

In many applications, the underlying data (the web, an XML document, or a relational database) can be seen as a graph. These graphs may be enriched with weights, associated with the nodes and edges of the graph, denoting application specific desirability/penalty assessments, such as popularity, trust, or cost. A particular challenge when considering such weights in query processing is that resu...

In this paper, we study the connectivity of the complement of a graph. We first establish a simple formula to compute the connectivity of a graph that comes from the join of graphs. Base on this formula, we give an upper and a lower bound to the connectivity of the complement of a graph. Keyword: connectivity, complement, join, vertex of attachment.

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset˜Ω. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...

We consider linear interval routing schemes studied by [3, 5] from a graph-theoretic perspective. We examine how the number of linear intervals needed to obtain shortest path routings in networks is affected by the product, join and composition operations on graphs. This approach allows us to generalize some of the results of [3, 5] concerning the minimum number of intervals needed to achieve s...

Subgraph enumeration, which aims to find all the subgraphs of a large data graph that are isomorphic to a given pattern graph, is a fundamental graph problem with a wide range of applications. However, existing sequential algorithms for subgraph enumeration fall short in handling large graphs due to the involvement of computationally intensive subgraph isomorphism operations. Thus, some recent ...

We prove that perfect graphs with no balanced skew-partitions admits a O(n) Clique-Stable separator. We then prove that for every graph G in this class, there always exists two subsets of vertices V1, V2 such that |V1|, |V2| ≥ c|V (G)| for some constant c and V1 is either complete or anticomplete to V2. The method uses trigraphs, introduced by Chudnovsky [5], and relies on the good behavior of ...

An r-dynamic coloring of a graph G is proper c the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each v ∈ V(G). The chromatic number minimum k has an with colors. In this paper, we obtain δ-dynamic central vertex join two graphs.