Dániel Korándi

Ks,t-saturated bipartite graphs

Abstract An n -by- n bipartite graph is H -saturated if the addition of any missing edge between its two parts creates a new copy of H . In 1964, Erdős, Hajnal and Moon made a conjecture on the minimum number of edges in a K s , s -saturated bipartite graph. This conjecture was proved independently by Wessel and Bollobas in a more general, but ordered, setting: they showed that the minimum number of edges in a K ( s , t ) -saturated bipartite graph is n 2 − ( n − s + 1 ) ( n − t + 1 ) , where K ( s , t ) is the “ordered” complete bipartite graph with s vertices in the first color class and t vertices in the second. However, the very natural question of determining the minimum number of edges in the unordered K s , t -saturated case remained unsolved. This problem was considered recently by Moshkovitz and Shapira who also conjectured what its answer should be. In this short paper we give an asymptotically tight bound on the minimum number of edges in a K s , t -saturated bipartite graph, which is only smaller by an additive constant than the conjecture of Moshkovitz and Shapira. We also prove their conjecture for K 2 , 3 -saturation, which was the first open case.

A Random Triadic Process

Given a random 3-uniform hypergraph

Decomposing random graphs into few cycles and edges

H=H(n,p)

Rainbow Saturation and Graph Capacities

on

A RANDOM TRIADIC PROCESS

n

On the Turán number of some ordered even cycles

vertices where each triple independently appears with probability

On the Turán number of ordered forests

p

Saturation in random graphs

, consider the following graph process. We start with the star

Separating path systems

G_0

Improved Ramsey-type results in comparability graphs

on the same vertex set, containing all the edges incident to some vertex