We introduce a parameter that measures the “constrainedness” of an ensemble of
combinatorial problems. If problems are over-constrained, they are likely to be insoluble. If …

Let $ G (n, m) $ be the random graph on $ n $ vertices with $ m $ edges. Let $ d= 2m/n $ be
its average degree. We prove that $ G (n, m) $ fails to be $ k $-colorable with high probability …

It is known that random k-SAT instances with at least cn clauses where c= ck is a suitable
constant are unsatisfiable (with high probability). We consider the problem to certify …

It is known that random k-SAT instances with at least cn clauses, where c=\nobreakc_k is a
suitable constant, are unsatisfiable (with high probability). We consider the problem to certify …

We look at the minimal size of a maximal matching in general, bipartite and d-regular
random graphs. We prove that with high probability the ratio between the sizes of any two …

It is known that random k-SAT instances with at least dn clauses where d= dk is a suitable
constant are unsatisfiable (with high probability). This paper deals with the question to certify …

Threshold Phenomena in Random Graph Colouring and Satisfiability by Dimitris Achlioptas A
thesis submitted in conformity with th Page 1 Threshold Phenomena in Random Graph …

Graph minors and the theory of graphs embedded in surfaces are fundamentally
interconnected. Robertson and Seymour used graph minors to prove a generalization of the …

In this paper we consider the problem of establishing a value $ r_0 $ such that almost all
random graphs with $ n $ vertices and $ rn $ edges, $ r> r_0 $, are asymptotically not 3 …

arXiv:math/0209087v1 [math.CO] 9 Sep 2002 Page 1 arXiv:math/0209087v1 [math.CO] 9 Sep
2002 On the non-3-colourability of random graphs. Olivier Dubois ∗ Jacques Mandler† …