3 problems

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Minimum dominating set conjecture for three-dimensional simplicial rook graphs
The simplicial rook graph ${\rm \mathcal{SR}}(3,n)$ has as vertices the vectors in $\mathbb{N}^3$ whose coordinates sum to $n$ , with two vertices adjacent when they differ in exact…
Conjectureopendomination graph-theory rook-graphsarXiv posted 2 days ago
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Martin and Wagner's integrality conjecture for simplicial rook graphs
The simplicial rook graph ${\rm \mathcal{SR}}(m,n)$ has as vertices the vectors in $\mathbb{N}^m$ whose coordinates sum to $n$ , with two vertices adjacent when they differ in exact…
Conjectureopengraph-theory rook-graphs spectral-graph-theoryarXiv posted 2 days ago
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The rook graph conjecture for lazy cop number
Rook graph conjecture. The unique smallest graph for which $c_L=n$ is
Conjectureopencop-number graph-theory rook-graphsarXiv posted 2 days ago

Minimum dominating set conjecture for three-dimensional simplicial rook graphs