We find arbitrarily large finite sets S of points in general position in the plane with the following property. If the points of S are equitably 2-colored (i.e., the sizes of the two color classes differ by at most one), then there is a polygonal line consisting of straight-line segments with endpoints in S, which is Hamiltonian, non-crossing, and alternating (i.e., each point of S is visited e...

We present a self-contained proof that the number of diameter pairs among n points in Euclidean 3-space is at most 2n − 2. The proof avoids the ball polytopes used in the original proofs by Grünbaum, Heppes and Straszewicz. As a corollary we obtain that any three-dimensional diameter graph can be embedded in the projective plane. Let S be a set of n points of diameter D in Rd. Define the diamet...

Internet worms pose a major threat to Internet infrastructure security, and their destruction will be truly costly. Therefore, the networks must be protected as much as possible against such attacks. In this paper we propose automatic and accurate system for signature generation for unknown polymorphic worms. We have designed a novel double-honeynet system, which is able to detect new worms tha...

The class of bipartite permutation graphs is the intersection of two well known graph classes: bipartite graphs and permutation graphs. A complete bipartite decomposition of a bipartite permutation graph is proposed in this note. The decomposition gives a linear structure of bipartite permutation graphs, and it can be obtained in O(n) time, where n is the number of vertices. As an application o...

An explicit definition of a 1-factorization of B k (the bipartite graph defined by the kand (k+l)-element subsets of [ 2k+ l ] ) , whose constituent matchings are defined using addition modulo k + 1, is introduced. We show that the matchings are invariant under rotation (mapping under ~r = (1, 2, 3 ..... 2k + 1 )), describe the effect of reflection (mapping under p = (1, 2k + 1)(2, 2k).. . (k, ...

Given graphs G and H, we define an H-packing of G to be a partition of the edges of G into some copies of H along with a set of edges L, called the leave. An H-packing is called maximum when |L| is minimum, or equivalently, when the H-packing contains as many copies of H as possible. A k-star, denoted Sk, is defined to be the complete bipartite graph K1,k. In this paper we characterize the numb...

We present an efficient fixed-parameter algorithm for #SAT parameterized by the incidence treewidth, i.e., the treewidth of the bipartite graph whose vertices are the variables and clauses of the given CNF formula; a variable and a clause are joined by an edge if and only if the variable occurs in the clause. Our algorithm runs in time O(4 k l N), where k denotes the incidence treewidth, l deno...

The linear discrepancy of a poset P , denoted ld(P ), is the minimum, over all linear extensions L, of the maximum distance in L between two elements incomparable in P . We prove that ld(P ) ≤ ⌊(3r − 1)/2⌋ when P has width 2. Tanenbaum, Trenk, and Fishburn asked whether this upper bound holds for all posets. We answer this in the negative by giving a randomized construction of bipartite posets ...

Connected bipartite permutation graphs without vertex labels are investigated. First, the number of connected bipartite permutation graphs of n vertices is given. Based on the number, a simple algorithm that generates a connected bipartite permutation graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected bipartite permutation graphs is proposed....

A graph is 1-extendible if every edge has a 1-factor containing it. A 1-extendible non-bipartite graph G is said to be near bipartite if there exist edges e1 and e2 such that G − {e1, e2} is 1-extendible and bipartite. We characterise the Pfaffian near bipartite graphs in terms of forbidden subgraphs. The theorem extends an earlier characterisation of Pfaffian bipartite graphs.