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**public sources and our publisher partners.**We consider the following probabilistic model of a graph on n labeled vertices. . First choose a random graph Gn ,1 r 2 ,and then choose randomly a subset Q of vertices of size k and force it to be a… Expand

Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake,… Expand

A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an… Expand

In this paper we study degree conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by… Expand

The Ramsey number rk(s, n) is the minimum N such that every red-blue coloring of the k-tuples of an N -element set contains a red set of size s or a blue set of size n, where a set is called red… Expand

For a graph $H$ and an integer $n$, the Turan number $\ex(n,H)$ is the maximum possible number of edges in a simple graph on $n$ vertices that contains no copy of $H$. $H$ is $r$-degenerate if every… Expand

A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath} \pagestyle{empty}… Expand

Let F (n, r, k) denote the maximum possible number of distinct edge-colorings of a simple graph on n vertices with r colors which contain no monochromatic copy of Kk .I t is shown that for every… Expand

It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d2/f is at most… Expand

In this article we study Hamilton cycles in sparse pseudorandom graphs. We prove that if the second largest absolute value of an eigenvalue of a d-regular graph G on n vertices satisfies