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...

Abstract: The wheel graph is the join of a single vertex and a cycle, while the fan graph is the join of a single vertex and a path. The resistance distance between any two vertices of a wheel and a fan are obtained. The resistances are related to Fibonacci numbers and generalized Fibonacci numbers. The derivation is based on evaluating determinants of submatrices of the Laplacian matrix. A com...

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 ...

In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to class digraphs and several results for vertex colorings in digraphs. Although, as a consequence these results, digraph can be obtained by constructions (directed identifying non-adjacent vertices), determining obtain is complex problem. particular, et posed problem operations construct symmetric 5-cycle from complete orde...

To be able to handle the ever growing volumes of XML documents, effective and efficient data management solutions are needed. Managing XML data in a relational DBMS has great potential. Recently, effective relational storage schemes and index structures have been proposed as well as special-purpose join operators to speed up querying of XML data using XPath/XQuery. In this paper, we address the...

We consider a closed fork and join queueing network where several lines feed a single assembly station. Under the assumption that at least one service time distribution is subexponential, we obtain the tail asymptotics of transient cycle times and waiting times. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary cycle times and waiting ...