Kreweras’ conjecture [9] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle of Qd. We [5] proved this conjecture but here we present ...
For planar graphs, counting the number of perfect matchings (and hence determining whether there exists a perfect matching) can be done in NC [4, 10]. For planar bipartite graphs, ...
This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our f...
Oswin Aichholzer, Sergey Bereg, Adrian Dumitrescu,...
We prove that monotone circuits computing the perfect matching function on n-vertex graphs require (n) depth. This implies an exponential gap between the depth of monotone and non...