As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle
problem has been the subject of intensive research. Recent developments in the area have …

The blow-up lemma states that a system of super-regular pairs contains all bounded degree
spanning graphs as subgraphs that embed into a corresponding system of complete pairs …

The classical Corrádi‐Hajnal theorem claims that every n‐vertex graph G with contains a
triangle factor, when. In this paper we present two related results that both use the absorbing …

An $ n $-vertex graph $ G $ is a $ C $-expander if $| N (X)|\geq C| X| $ for every $
X\subseteq V (G) $ with $| X|< n/2C $ and there is an edge between every two disjoint sets of …

We show that every $(n, d,\lambda) $-graph contains a Hamilton cycle for sufficiently large $
n $, assuming that $ d\geq\log^{10} n $ and $\lambda\leq cd $, where $ c=\frac {1}{9000} …

Abstract Extremal Graph Theory is a very deep and wide area of modern combinatorics. It is
very fast developing, and in this long but relatively short survey we select some of those …

For a graph G on n⩾ 18 vertices and e (G) edges that does not contain the 2-power of a
Hamilton cycle C n 2, we identify all the graphs G with e (G)= ex (n, C n 2)− 1 and e (G)= ex …

The study of sum and product problems in finite fields motivates the investigation of additive
structures in multiplicative subgroups of such fields. A simple known fact is that any …

A famous conjecture of Pósa from 1962 asserts that every graph on n vertices and with
minimum degree at least 2n/3 contains the square of a Hamilton cycle. The conjecture was …

We prove that, for any t≥ 3, there exists a constant c= c (t)> 0 such that any d-regular n-
vertex graph with the second largest eigenvalue in absolute value λ satisfying λ≤ cdt− 1/nt …