We study the following min-min random graph process G = (G0, G1, . . .): the initial state G0 is an empty graph on n vertices (n even). Further, GM+1 is obtained from GM by choosing a pair {v, w} of distinct vertices of minimum degree uniformly at random among all such pairs in GM and adding the edge {v, w}. The process may produce multiple edges. We show that GM is asymptotically almost surely...

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by using not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NP-hardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provide...

We consider combinatorial optimization problems with uncertain objective functions. In the min-max-min robust optimization approach, a fixed number k of feasible solutions is computed such that the respective best of them is optimal in the worst case. The idea is to calculate a set of candidate solutions in a potentially expensive preprocessing and then select the best solution out of this set ...

We give the first, as far as we know, feasible proof of König’s Min-Max Theorem (KMM), a fundamental result in combinatorial matrix theory, and we show the equivalence of KMM to various Min-Max principles, with proofs of low complexity.