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This is a short note of something that I wasn’t sure whether it is true for infinite graphs. Let be any simple, undirected graph, finite or infinite, such that . By we denote the complement of . Proposition. At least … Continue reading
Encouraged by Eric S. Raymond’s book The Art of Unix Programming I have started using ed. My affection for it keeps growing. To begin with, it is the prime example of minimality, a property that is cherished all over the … Continue reading
Motivation. I stumbled over the following hypergraph coloring concept when reading about an old (and open) problem by Erdos and Lovasz. Let be a hypergraph such that for all we have , and let be a set. Then a map … Continue reading
Ein Ereignis ist in diesen Sommertagen etwas in Vergessenheit geraten: Vor 2500 Jahren hat der Grieche Heliotides die Sonne entdeckt. Aus heutiger Sicht schwer zu glauben, dass diese Entdeckung eines grossen Kopfes bedurfte – aber schliesslich hatte es auch einen … Continue reading
Homogeneous spaces are topological spaces that locally look everywhere the same. Put in mathematical terms, is homogeneous if for any there is an isomorphism such that . We can generalize this by not restricting ourselves to a pair of points … Continue reading
In this presentation by Martín Escardó I came across a nice concept of continuity in the set of all functions . For and we say that if and only if for all we have . Then we define to be finitely … Continue reading
Let be a finite, simple, undirected graph. Hadwiger’s conjecture states that if then is a minor of . Let’s call that statement (Hadw). We show that it is equivalent to the following statement: (Hadw’): If is not a complete graph, … Continue reading