منابع مشابه
Some combinatorial problems of importance
We discuss two combinatorial problems for which we have only sub-optimal solutions. We describe known solutions and we explain why better solutions would be of importance to Cryptography. The areas of application are in improving the ef-ciency of Zero-Knowledge proofs, in relating the quadratic residuosity problem to the problem of integer factorization, and in analyzing some cryptographic sche...
متن کاملOn some metric and combinatorial geometric problems
I have published many papers on this and related topics [1] . Important progress has been made over the last few years on many of these problems and I will give a short review of some of these at the end of this paper and also state there some of the remaining problems, but first of all I will state some new problems . Usually we will restrict ourselves to the plane though many interesting ques...
متن کاملSome Combinatorial Problems on Halin Graphs
Let T be a tree with no degree 2 vertices and L(T) = {l1,. .. , lr}, r ≥ 2 denote the set of leaves in T. An Halin graph G is a graph obtained from T such that V (G) = V (T) and E(G) = E(T) ∪ {{li, li+1} | 1 ≤ i ≤ r − 1} ∪ {l1, lr}. In this paper, we investigate combinatorial problems such as, testing whether a given graph is Halin or not, chromatic bounds, an algorithm to color Halin graphs wi...
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We state and discuss various problems in the general area of arithmetic combinatorics and recent developments related to the ‘sum-product phenomenon’ in the ring of integers, the real and complex numbers and finite fields. In particular, we discuss applications and connections to the theory of exponential sums, Burgess’ estimate, the subspace theorem and to Szemeredi-Trotter type results. In re...
متن کاملSome Combinatorial Problems in the Plane
1 Let there be given n points in the plane. Denote by t i the number of lines which contain exactly i of the points (2 < i < n). The properties of the set {ti } have been studied a great deal. For example, there is the classical result of Gallai and Sylvester : Assume to = 0 (i .e ., the points are not all on one line) ; then t2 > 0. For the history of this problem see, e.g ., Motzkin [6] and E...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1956
ISSN: 0002-9939
DOI: 10.2307/2033030