A recent comparison of evolutionary, neural network, and scatter search heuristics for solving the p-median problem is completed by (i) gathering or obtaini...

The probabilistic satisfiability problem is to verify the consistency of a set of probability values or intervals for logical propositions. The (tight) prob...

We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of <i>L</i>₂-n...

A set of vertices <i>S</i> in a graph <i>G</i> is independent if no neighbor of a vertex of <i>S</i> belongs to <i>S</i>. A set of vertices <i>U</i> in a gr...

This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequential form of...

The AutoGraphiX 2 system is used to compare the index of a graph <i>G</i> with a number of other graph theoretical invariants, i.e., chromatic number, maxim...

A graph invariant is a function of a graph <i>G</i> which does not depend on labeling of <i>G</i>’s vertices or edges. An algebraic expression of one or sev...

Assouad has shown that a real-valued distance <i>d</i> = (<i>d</i>_<i>ij</i>) _{1 &le; <i>i</i> &lt; <i>j</i> &le; <i>n</i>} is isome...

The value <img src="/cgi-bin/mimetex.cgi?\frac{1}{2n} \cot\left( \frac{\pi}{2n}\right)"> is shown to be an upper bound on the width of any <i>n</i>-sided p...

A set of vertices <i>S</i> in a graph <i>G</i> is independent if no neighbor of a vertex of <i>S</i> belongs to <i>S</i>. The independence number &alpha is ...

From the pentagon onwards, the area of the regular convex polygon with <i>n</i> sides and unit diameter is greater for each odd number <i>n</i> than for the...

We consider four conjectures related to the largest eigenvalue of (the adjacency matrix of) a graph (i.e., to the index of the graph). Three of them have be...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)">&nbsp; be a simple graph with vertex degrees &nbsp;<img src="/cgi-bin/mimetex.cgi?d1, d2, \ldots, d_n...

Let &nbsp;<img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple graph with &nbsp;<img src="/cgi-bin/mimetex.cgi?n=|V|"> vertices and &nbsp;<img src="/cgi-bin/...

Given a simple connected graph <i>G = (V,E)</i> the geodetic closure <i>I&nbsp;[S]</i> <img src="/cgi-bin/mimetex.cgi?\subset"> <i>V</i> of a subset <i>S</i...

We discuss feature selection approaches within the context of linear programming models for discrimination, with special emphasis on a new interpretation an...

The AutoGraphiX research program led to a new type of application of metaheuristics in graph theory, <i>i.e.</i>, finding conjectures on graph invariants by...

Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form <img src="/cgi-bin/mimetex.cgi?lbn \leq R \oplus i \leq ub...

Colour image quantization is a data compression technique that reduces the total set of colours in an image to a representative subset. This problem is expr...

We consider the problem of separating two sets of points in an Euclidean space with a hyperplane that minimizes the sum of <i>L_p</i>-norm distanc...