The Anari-Oveis Gharan-Vinzant perfect-matching entropy conjecture

Lineage and corrections

Anari, Oveis Gharan and Vinzant, arXiv 1807.00929 evidence for this event

Theorem 1.1: for a loopless multigraph on $2m\ge2$ vertices with a perfect matching and every $x\in P(G)$, boundary included, $F(x)-(2-2/m)B(x)\le H(x)\le F(x)$, where $H(x)$ is the maximum entropy of a law on perfect matchings with marginals $x$. Hence $\log N(G)\le\max_{x\in P(G)}(F+B)\le\log N(G)+3m-2$, the conjectured linear error with an explicit constant. Also proved: the sharp bound $|\mathrm{supp}\,x|-\dim F_x\le3m-2$ for the minimal face, and lower counts such as $N(G)\ge e^{-2(m-1)}k^m$ for $k$-regular graphs with all odd cuts of size at least $k$. The paper notes the bipartite coefficient-one inequality $H\ge F-B$ fails for a nonbipartite eight-vertex example. parent of this event

This event attributed to Unreleased internal OpenAI model

Lean Comparator challenge MatchingEntropyBounds (sharp pointwise bound) evidence for this event

VibeMathed record: The Anari-Oveis Gharan-Vinzant perfect-matching entropy conjecture evidence for this event

Same family: A Fully Polynomial Randomized Approximation Scheme for Perfect Matchings in General Graphs evidence for this event

Lean (catalogued): OAI.MatchingEntropy.entropy_main evidence for this event

The Anari-Oveis Gharan-Vinzant perfect-matching entropy conjecture parent of this event

The Anari-Oveis Gharan-Vinzant perfect-matching entropy conjecture evidence for this event