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...

A glued graph at K2-clone (K3-clone) results from combining two vertex-disjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers of glued graphs at K2-clones and K3-clones in terms of the clique partition numbers of their orig...

Let G = (V (G), E(G)) be an undirected graph with a measure function μ assigning non-negative values to subgraphs H so that μ(H) does not exceed the clique cover number of H. When μ satisfies some additional natural conditions, we study the problem of separating G into two subgraphs, each with a measure of at most 2μ(G)/3 by removing a set of vertices that can be covered with a small number of ...

We consider the (r, l)-Partization problem of finding a set of at most k vertices whose deletion results in a graph that can be partitioned into r independent sets and l cliques. Restricted to perfect graphs and split graphs, we describe sequacious fixed-parameter tractability results for (r, 0)-Partization, parameterized by k and r. For (r, l)-Partization where r + l = 2, we describe an O∗(2k)...

This work presents methods for interconnect optimization while performing register optimization and placement of registers in memory. It has been shown that the port assignment problem is similar to the register optimization problem that also considers interconnect optimization. The basic formulation of the register-interconnect optimization problem has been posed as that of finding a clique co...

Mining dense subgraphs on multi-layer graphs is aninteresting problem, which has witnessed lots of applications inpractice. To overcome the limitations of the quasi-clique-basedapproach, we propose d-coherent core (d-CC), a new notionof dense subgraph on multi-layer graphs, which has severalelegant properties. We formalize the diversified coherent coresearch (DCCS) probl...

In the previous lecture we covered polynomial time reductions and approximation algorithms for vertex cover and set cover problems. By reductions we showed that SAT, 3SAT, Independent Set, Vertex Cover, Integer Programming, and Clique problems are NP-Hard. In this lecture we will continue to cover approximation algorithms for maximum coverage and metric TSP problems. We will also cover Strong N...

Trapezoid graphs are a class of cocomparability graphs containing interval graphs and permutation graphs as subclasses. They were introduced by Dagan, Golumbic and Pinter DGP]. They propose an O(n 2) algorithm for chromatic number and a less eecient algorithm for maximum clique on trapezoid graphs. Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, ...

In this paper we study the edge-thickness and the clique-thickness of a graph. The edge-thickness of a graph is defined as the thickness of the family of edges. The clique-thickness of a graph is defined as the thickness of the family of maximal cliques. Edges and maximal cliques of a graph are both considered as a collection of subsets of the vertex set. On one hand, we introduce a new paramet...