A basic elementary extension of the Duchet–Meyniel theorem

A basic elementary extension of the Duchet-Meyniel theorem

The Conjecture of Hadwiger implies that the Hadwiger number h times the independence number α of a graph is at least the number of vertices n of the graph. In 1982 Duchet and Meyniel proved a weak version of the inequality, replacing the independence number α by 2α− 1, that is, (2α− 1) · h ≥ n. In 2005 Kawarabayashi, Plummer and the second author published an improvement of the theorem, replaci...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

A FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials