A Minimal Edge Cover is an Edge Cover such that no other Edge Cover is a proper subset of it.
- Which is the complexity of counting Minimal Edge Covers? Do we know any non-trivial upper bound on their number? Is there any clever algorithm in literature to enumerate them?
- Empirically, I'm observing that the number of Minimal Edge Covers seems to be always odd: so far in my experiments I've never met a graph having an even number of them. Is this a theoretically proven fact? If not, has their parity been investigated in literature?