Given a cardinal κ and a sequence (αi )i∈κ of ordinals, we determine the least ordinal (when one exists) such that the topological partition relation

The resolution complexity of the perfect matching principle was studied by Razborov [Raz04], who developed a technique for proving its lower bounds for dense graphs. We construct a a constant degree bipartite graph Gn such that the resolution complexity of the perfect matching principle for Gn is 2 Ω(n), where n is the number of vertices inGn. This lower bound matches with the upper bound 2 O(n...

The resolution complexity of the perfect matching principle was studied by Razborov [Raz04], who developed a technique for proving its lower bounds for dense graphs. We construct a a constant degree bipartite graph Gn such that the resolution complexity of the perfect matching principle for Gn is 2 Ω(n), where n is the number of vertices inGn. This lower bound matches with the upper bound 2 O(n...

Discrete Mathematics deals with finite or countable sets, and thus, in particular, with natural numbers. This mathematical field bring into play several overlapping domains, e.g. number theory (arithmetic and combinatorics), graph theory, and combinatorial geometry. As a consequence of the peculiarities of discreteness versus continuum, interesting specific reasonings can be developed (Batanero...