We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let Gn,p be a random graph, and let S be a set consis...
Abstract. We show that a maximum cut of a random graph below the giantcomponent threshold can be found in linear space and linear expected time by a simple algorithm. In fact, the ...
The adaption of combinatorial duality to infinite graphs has been hampered by the fact that while cuts (or cocycles) can be infinite, cycles are finite. We show that these obstruc...
We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather diffe...
Abstract. The main results of this paper are regularity and counting lemmas for 3uniform hypergraphs. A combination of these two results gives a new proof of a theorem of Frankl an...