# ZarankiewiczDB,

an online database of Zarankiewicz numbers.

## z(18,22) = 91

Searching for matrices of weight greater than 91, all but 6 scaffolds were eliminated without search.

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,3,2)$, $\mathbf{n}=(4,4,4)$, $m_O=0$, $n_O=4$.

(26.225512739 seconds, score = 0, 147577 recursive calls, max depth = 29)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,3,2)$, $\mathbf{n}=(5,4,4)$, $m_O=0$, $n_O=3$.

(5.182624328 seconds, score = 0, 29249 recursive calls, max depth = 24)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,2,2)$, $\mathbf{n}=(4,4,4)$, $m_O=1$, $n_O=4$.

(81.463914547 seconds, score = 0, 444599 recursive calls, max depth = 31)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,2,2)$, $\mathbf{n}=(5,4,4)$, $m_O=1$, $n_O=3$.

(0.738657287 seconds, score = 0, 3938 recursive calls, max depth = 24)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,3,1)$, $\mathbf{n}=(4,4,4)$, $m_O=1$, $n_O=4$.

(10.728529185 seconds, score = 0, 59985 recursive calls, max depth = 32)

Scaffold: $p=5$, $q=3$, $\mathbf{m}=(3,3,3,3,1)$, $\mathbf{n}=(5,4,4)$, $m_O=1$, $n_O=3$.

(0.124918111 seconds, score = 0, 647 recursive calls, max depth = 22)

upper bound = 91, submitted by Andrew Kay on April 22nd, 2016 (link)

By adding a column of weight 1 to z(18,21).

lower bound = 91, submitted on April 22nd, 2016 (link)

Submit a result or comment?