the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

2 The Linearity of Expectation and small tweakings 11 2.1 Revisiting the Ramsey Number R(n, n) . . . . . . . . . . . . . . . . . . . 11 2.2 List Chromatic Number and minimum degree . . . . . . . . . . . . . . . 11 2.3 The Daykin-Erdős conjecture . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 An Example from Combinatorial Geometry . . . . . . . . . . . . . . . . . 14 2.5 Graphs with High...

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Preface This manuscript contains my personal and informal notes on the probabilistic method as it is applied in graph theory. It hasn't been properly proofread , and it is by no means intended for wider distribution. For an introduction to the probabilistic method, I refer the reader to the textbooks mentioned in the bibliography. I'm very grateful for the assistance and advice I have received ...

The probabilistic method is an efficient technique to prove the existence of combinatorial objects having some specific properties. It is based on the probability theory but it can be used to prove theorems which have nothing to do with probability. The probabilistic method is now widely used and considered as a basic knowledge. It is now exposed in many introductory books to graph theory like ...