4,897 research outputs found
Linear trees in uniform hypergraphs
Given a tree T on v vertices and an integer k exceeding one. One can define
the k-expansion T^k as a k-uniform linear hypergraph by enlarging each edge
with a new, distinct set of (k-2) vertices. Then T^k has v+ (v-1)(k-2)
vertices. The aim of this paper is to show that using the delta-system method
one can easily determine asymptotically the size of the largest T^k-free
n-vertex hypergraph, i.e., the Turan number of T^k.Comment: Slightly revised, 14 pages, originally presented on Eurocomb 201
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
A coding problem for pairs of subsets
Let be an --element finite set, an integer. Suppose that
and are pairs of disjoint -element subsets of
(that is, , , ). Define the distance of these pairs by . This is the
minimum number of elements of one has to move to obtain the other
pair . Let be the maximum size of a family of pairs of
disjoint subsets, such that the distance of any two pairs is at least .
Here we establish a conjecture of Brightwell and Katona concerning an
asymptotic formula for for are fixed and . Also,
we find the exact value of in an infinite number of cases, by using
special difference sets of integers. Finally, the questions discussed above are
put into a more general context and a number of coding theory type problems are
proposed.Comment: 11 pages (minor changes, and new citations added
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