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The complexity of the matching polytope of graphs may be measured with the maximum length β of a starting sequence of odd ears in an ear-decomposition. Indeed, a theorem of Edmonds and Pulleyblank shows that its facets are defined by 2-connected factor-critical graphs, which have an odd ear-decomposition (according to a theorem of Lovász). In particular, β(G) ≤ 1 if and only if the matching pol...

I In a short piece written most likely in the 1690s and given the title by Loemker of “On Wisdom,” Leibniz says the following: “...we see that happiness, pleasure, love, perfection, being, power, freedom, harmony, order, and beauty are all tied to each other, a truth which is rightly perceived by few.” Why is this? That is, why or how are these concepts tied to each other? And, why have so few ...