Building counterexamples

نویسنده

Irena Rusu

چکیده

A conjecture concerning perfect graphs asserts that if for a Berge graph G the following three conditions hold: 1. neither G, nor Ḡ has an even pair; 2. neither G, nor Ḡ has a stable cutset; 3. neither G, nor Ḡ has a star-cutset, then G or Ḡ is diamond-free. We show that this conjecture is not valid and that, in a way, every weaker version is false too. To this end, we construct a class of perfect graphs satisfying the hypothesis above and indicate counterexamples within this class for the instances of the conjecture obtained by replacing the diamond with any graph H which is the join of a clique and a stable set.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

COUNTEREXAMPLES IN CHAOTIC GENERALIZED SHIFTS

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

متن کامل

A loosely Bernoulli counterexample machine

In Rudolph’s paper on minimal self joinings [7] he proves that a rank one mixing transformation constructed by Ornstein [5] can be used as the building block for many ergodic theoretical counterexamples. In this paper we show that Ornstein’s transformation can be altered to create a general method for producing zero entropy, loosely Bernoulli counterexamples. This paper answers a question posed...

متن کامل

The Bernstein Conjecture, Minimal Cones, and Critical Dimensions

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we r...

متن کامل

Building Proofs or Counterexamples by Analogy in a Resoluton Framework

Taking an extension of resolution as a base calculus (though its principles are applicable to other calculi) for searching proofs (refuta-tions) and counterexamples (models), we introduce a new method able to nd refutations and also models by analogy with refutations and models in a knowledge base. The source objects for the analogy process are generalizations of the refutations (models). They ...

متن کامل