We show that a cubic graph G with girth g(G) ≥ 5 has a Hamiltonian Circuit if and only if the matrix A+ I can be row permuted such that each column has at most 2 blocks of consecutive 1’s, where A is the adjacency matrix of G, I is the unit matrix, and a block can be consecutive in circular sense, i.e., the first row and the last row are viewed as adjacent rows. Then, based on this necessary an...

We develop and demonstrate a probabilistic method for classifying rare objects in surveys with the particular goal of building very pure samples. It works by modifying the output probabilities from a classifier so as to accommodate our expectation (priors) concerning the relative frequencies of different classes of objects. We demonstrate our method using the Discrete Source Classifier, a super...

The theory of nite trees in nite signature is axiomatized by the simple set of axioms E : 1. 8x x 6 = t(x) for every non-variable term t(x) containing x, 2. 8x 8y (f(x) = f(y) , x = y) for every f 2 , 3. 8x 8y (f(x) 6 = g(y)) for diierent f, g 2 , plus the usual equality axioms, plus the following Domain Closure Axiom: 8x _ f2 9z (x = f(z)) (DCA) postulating that every element of a model is in ...

That this estimate of the order of magnitude at infinity cannot be essentially improved is shown by examples of the form z=f(x) —g(y), /">0, g">0, where/ and g can be chosen such that the order is just 0(r). A still open question is whether z(x, y) can or cannot be o(r) along a special sequence of radii r —>». In proving the theorem we shall, essentially, follow Bernstein's original arguments. ...

We introduce the logics E(G) for reasoning about probabilistic expectation over classes G of games with discrete polynomial payoff functions represented by finite-valued Lukasiewicz formulas and provide completeness and complexity results. In addition, we introduce a new class of games where players’ expected payoff functions are encoded by E(G)-formulas. In these games each player’s aim is to ...

Let S be a semigroup. The intersection graph of an S-act A, denoted by G(A), is the undirected simple graph obtained by setting all non-trivial subacts of A to be the vertices and defining two distinct vertices to be adjacent if and only if their intersection is non-empty. It is investigated the interplay between the algebraic properties of A and the graph-theoretic properties of G(A). Also som...

Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional calculus (propositional logic) in which proofs are combinatorial (graph-theoretic), rather than syntactic. It defines a combinatorial proof of a proposition φ as a graph homomorphism h : C → G(φ), where G(φ) is a graph associated with φ and C is a coloured...

A strong edge-colouring of a graph G is a proper edge-colouring such that every path of three edges uses three colours. An induced matching of a graph G is a subset I of edges of G such that the graph induced by the endpoints of I is a matching. In this paper, we prove the NP-completeness of strong 4, 5, and 6-edge-colouring and maximum induced matching in some subclasses of subcubic triangle-f...

Assume we are given a sub-integrable arrow v. In [7, 7], the authors extended quasi-reversible isometries. We show that g ≥ P . It is not yet known whether J is not equivalent to z̄, although [7] does address the issue of completeness. In this context, the results of [37, 18] are highly relevant.