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        Maximum number of perfect matchings in a graph of genus $g$ balanced $k$-partite graph

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        What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (number of vertices for each color in all possible $k$-colorings is within a difference of $1$) can have? I am particularly interested in $k=2$.

        For planar balanced bipartite graphs (each color has to have same number of vertices assigned) the number of perfect matchings is $2^{O(n)}$ while for genus $\Omega(n^2)$ we can have $2^{\Omega(n\log n)}$. So is maximum number of perfect matchings $2^{O(n\log g)}$ for $k=2$?

        What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (number of vertices for each color in all possible $k$-colorings is within a difference of $1$) can have? I am particularly interested in $k=2$.

        What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (number of vertices for each color in all possible $k$-colorings is within a difference of $1$) can have? I am particularly interested in $k=2$.

        For planar balanced bipartite graphs (each color has to have same number of vertices assigned) the number of perfect matchings is $2^{O(n)}$ while for genus $\Omega(n^2)$ we can have $2^{\Omega(n\log n)}$. So is maximum number of perfect matchings $2^{O(n\log g)}$ for $k=2$?

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        What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (equal numbernumber of vertices for each color in all possible $k$-colorings) is within a difference of genus $g$$1$) can have? I am particularly interested in $k=2$.

        What is the maximum number of perfect matchings a balanced $k$-partite graph (equal number of vertices for each color in all possible $k$-colorings) of genus $g$ can have? I am particularly interested in $k=2$.

        What is the maximum number of perfect matchings a genus $g$ balanced $k$-partite graph (number of vertices for each color in all possible $k$-colorings is within a difference of $1$) can have? I am particularly interested in $k=2$.

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        山西福彩快乐十分钟
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