IN this continuation of the special issue of papers invited from the Fifth International Workshop on Algorithms in Bioinformatics (WABI ’05), we present three papers which are summarized below. An alternative to the classical Hannenhali-Pevzner theory for sorting by reversal is described by Séverine Bérard, Anne Bergeron, Cedric Chauve, and Christophe Paul in their paper “Perfect Sorting by Rev...

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy, and random outcomes a...

Let L be a lattice. The annihilating-ideal graph of is simple whose vertex set the all nontrivial ideals and two distinct vertices I J are adjacent if only I∧J=0. In this paper, crosscap graphs lattices with at most four atoms characterized. These characterizations provide classes multipartite graphs, which embedded in Klein bottle.

In this note we give an algorithm which enables us to encode and enumerate all the spanning trees of a multipartite graph (see below). This algorithm may turn out to be useful for the enumeration of spanning trees satisfying certain conditions. The number of spanning trees of a given graph Γ without loops and without multiple edges will be denoted by_i(T). We shall consider the graphs Γ = T(G; ...

We show that there are polynomial-time algorithms to compute maximum independent sets in the categorical products of two cographs and two splitgraphs. The ultimate categorical independence ratio of a graph G is defined as limk→∞ α(G )/n. The ultimate categorical independence ratio is polynomial for cographs, permutation graphs, interval graphs, graphs of bounded treewidth and splitgraphs. When ...

In the paper we introduce a new variant of graph coloring game and parameter being result game. We study their properties get some lower upper bounds, exact values for complete multipartite graphs optimal, often polynomial-time strategies both players provided that is played on with an odd number vertices. At end show games, classic one, are related: our bound chromatic number.

A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination of a graph G the generating function number dominating sets each cardinality in G, have been conjectured unimodal. In this paper we will show paths, cycles complete multipartite graphs unimodal, that almost every with mode $$ \lceil \frac{n}{2}\rceil .

For a graph G, a partiteness k ≥ 2 and a number of colours c, we define the multipartite Ramsey number r k (G) as the minimum value m such that, given any colouring using c colours of the edges of the complete balanced k-partite graph with m vertices in each partite set, there must exist a monochromatic copy of G. We show that the question of the existence of r k (G) is tied up with what monoch...

Suppose Kv is the complete undirected graph with v vertices. Let K4 − e be the graph obtained from K4 by removing one edge. A (K4 − e) group divisible design (briefly (K4 − e)-GDD) of type h is a triple (X,G,B), where G is a partition of X into groups each of size h, B is an edge-disjoint decomposition of the edge set of Kh,h,...,h, the multipartite complete undirected graph with G as the parti...