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Question: what is known about minimum/maximum weight perfect matchings in magic squares with or without special properties like e.g. being pandiagonal? I am especially interested minimal/maximal ...

Let $n$ be the positive integer. Let $A$ and $B$ be sets of divisors of $n$ less and more than $\sqrt{n}$ respectively. Consider bipartite graph $(A, B)$, where two vertices are connected when one ...

Is there a $P$ time definable sequence of succinct polynomial sized representation of balanced bipartite graphs whose number of perfect matchings is a primorial? For factorial a complete bipartite ...

Given set $\mathcal T_n=\{0,1,\dots,2^n-1\}$ what is the minimum number of vertices $2m$ needed in a planar bipartite balanced graph such that at every $i\in\mathcal T_n$ there is a graph $G\in\...