Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NPcomplete to decide for general graphs. It has been recently proved that for cographs, the existence of such a partition can be characterized by finitely many forbidden subgraphs, and hence tested in polynomial time. In this paper ...

In Defective Coloring we are given a graph G and two integers χd,∆ ∗ and are asked if we can χd-color G so that the maximum degree induced by any color class is at most ∆∗. We show that this natural generalization of Coloring is much harder on several basic graph classes. In particular, we show that it is NP-hard on split graphs, even when one of the two parameters χd,∆ ∗ is set to the smallest...

A graphs G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irred...

We consider the following vertex-partition problem on graphs, known as the CLUSTER DELETION (CD) problem: given a graph with real nonnegative edge weights, partition the vertices into clusters (in this case, cliques) to minimize the total weight of edges outside the clusters. The decision version of this optimization problem is known to be NP-complete even for unweighted graphs and has been stu...

Read-once functions have gained recent, renewed interest in thefields of theory and algorithmsofBoolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A.Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. M...

In the literature, there are quite a few algorithms to solve problems on distance-hereditary graphs. Two well-known graphs, trees and cographs, both belong to the class of distance-hereditary graphs. In this paper, we present an O(|V | + |E|)-time sequential algorithm to solve the Hamiltonian problem on a distance-hereditary graph G = (V, E). This algorithm is faster than the previous best resu...

A multi-break rearrangement generalizes most of genome rearrangements, such as block-interchanges, transpositions and reversals. A k-break cuts k adjacencies over a permutation, and forms k new adjacencies by joining the extremities according to an arbitrary matching. Block-interchange distance is a polynomial problem, but the transposition and the reversal distances are both NP-hard problems. ...

Modern biotechnological tools are essential to combat against the plant parasitic nematodes. In modern functional genomics era some of the important tools that are being used by researchers are RNA interference (RNAi), microRNAs, transcriptome profiling, genome squencing etc. Besides these, transformation of cultivated species with cloned nematode resistance genes is another approach to create ...

A graph on n vertices is -far from a property P if one has to add or delete from it at least n edges to get a graph satisfying P. A graph property P is strongly testable (in the dense model) if for every fixed > 0 it is possible to distinguish, with one-sided error, between graphs satisfying P and ones that are -far from P by inspecting the induced subgraph on a random subset of at most f( ) ve...

Recent characterization [9] of those graphs for which coloured MSO2 model checking is fast raised the interest in the graph invariant called tree-depth. Looking for a similar characterization for (coloured) MSO1, we introduce the notion of shrub-depth of a graph class. To prove that MSO1 model checking is fast for classes of bounded shrub-depth, we show that shrub-depth exactly characterizes th...