A Sample Article for the Monthly 1 Introduction. (2009)
Daniel J. Velleman, Paul Erdős
This sample article explains and illustrates many of the conventions you should follow in preparing the final version of your paper for the Monthly. There is no need to try to imitate the appearance...
1 Introduction. A Sample Note for the Monthly (2008)
Daniel J. Velleman, Paul Erdős
This sample note explains and illustrates many of the conventions you should follow in preparing the final version of your paper for the Monthly. There is no
RANDOM GRAPH ISOMORPHISM* (2008)
László Babali, Paul Erdős, M Selkow
Abstract. A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but o(2 (2>) of the 2 t 1 graphs on n vertices). Hence, for almost all graphs...
©North-Holland Publishing Company REPRESENTATION OF GROUP ELEMENTS AS SHORT PRODUCTS (2008)
Dedicated to Professor A. Kotzig on the occasion of his sixtieth birthday We prove that every group G of order n has t,log n/log 2+0dog log n) elements x, x, such that every group element is a...
REGULAR PAIRS IN SPARSE RANDOM GRAPHS I Y. KOHAYAKAWA AND V. R (2008)
Dedicated Professor, Paul Erdős
Abstract. We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemerédi and, among other things, show that they must satisfy a certain local pseudorandom...
REGULAR PAIRS IN SPARSE RANDOM GRAPHS I Y. KOHAYAKAWA AND V. R (2008)
Dedicated Professor, Paul Erdős
Abstract. We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemerédi and, among other things, show that they must satisfy a certain local pseudorandom...
Paul Erdős (1913–1996) 1. Prologue (2007)
Polynomials T. Erdélyi, Paul Erdős, Paul Erdős, Interpolation P. Vértesi
at Kerepesi Cemetery in Budapest to pay their last respects to Paul Erdős. If there was one theme suggested by the farewell orations, it was that the world of mathematics had lost a legend, one of...
On cycles in the coprime graph of integers 1 (2007)
Dedicated to Herbert S. Wilf on the occasion of his 65 th birthday In this paper we study cycles in the coprime graph of integers. We denote by f(n, k) thenumberofpositiveintegersm≤nwithaprime...
ON THE NUMBER OF DIVISORS OF n! (2007)
Paul Erdős, S. W. Graham, Ar Ivić, Carl Pomerance
Abstract. Several results involving d(n!) are obtained, where d(m) denotes the number of positive divisors of m. These include estimates for d(n!)/d((n − 1)!), d(n!) − d((n − 1)!), as well as...
On k-saturated graphs with restrictions on the degrees (1996)
Noga Alon, Paul Erdős, Ron Holzman, Michael Krivelevich
A graph G is called k-saturated, where k ≥ 3 is an integer, if G is K k-free but the addition of any edge produces a K k (we denote by K k a complete graph on k vertices). We investigate...
Paul Erdős, László Babai, Carl Pomerance, Péter Vértesi, Paul Erdős Number, Carl Pomerance
a memorial article appears elsewhere in this issue. This feature article gives a cross section of his monumental oeuvre. Most of Erdős’s work falls roughly into the following categories: •...
Boris Aronov, Paul Erdős, Wayne Goddard, Daniel J. Kleitman, Michael Klugerman, János Pach, ...
Given a set of points in the plane, a crossing family is a collection of line segments, each joining two of the points, such that any two line segments intersect internally. Two sets A and B of...
Hungarian Academy ofSciences (1986)
Paul Erdős, Ralph Faudree, Edward T Ordman
Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph. For a graph on n vertices, the clique partition number can grow cn z times as fast as the...
North-Holland PROBLEMS AND RESULTS IN COMBINATORIAL ANALYSIS AND GRAPH THEORY (1986)
I wrote many papers with this and similar titles. In my lecture I stated several of my old solved and unsolved problems some of which have already been published elsewhere. To avoid overlap as much...
On sums of Rudin-Shapiro coefficients II (1983)
Brillhart, John, Erdős, Paul, Morton, Patrick
Let {a(n)} be the Rudin-Shapiro sequence, and let s(n) = ∑a(k) and t(n) = ∑(-1)k a(k). In this paper we show that the sequences {s(n)/√n} and {t(n)/√n} do not have cumulative distribution...
Supersaturated graphs and hypergraphs (1983)
We shall consider graphs (hypergraphs) without loops and multiple edges. Let Ybe a family of so called prohibited graphs and ex (n, Y) denote the maximum number of edges (hyperedges) a graph...
Some bounds for the Ramsey-Paris-Harrington numbers (1981)
It has recently been discovered that a certain variant of Ramsey's theorem cannot be proved in first-order Peano arithmetic although it is in fact a true theorem. In this paper we give some...