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of a vertex in $G$. We show that, (i) $lbox(G) \leq 2^{13\log^{*}{\Delta}} \Delta$. There exist graphs of maximum degree $\Delta$ having a local boxicity of $\Omega(\frac{\Delta}{\log\Delta})$. (ii) $lbox(G ...
of a vertex in $G$. We show that, (i) $lbox(G) \leq 2^{13\log^{*}{\Delta}} \Delta$. There exist graphs of maximum degree $\Delta$ having a local boxicity of $\Omega(\frac{\Delta}{\log\Delta})$. (ii) $lbox(G ...
that all graphs of maximum degree $\Delta$ have local boxicity $O(\Delta)$, while almost all graphs of maximum degree $\Delta$ have local boxicity $\Omega(\Delta)$, improving known upper and lower bounds. We ...
that all graphs of maximum degree $\Delta$ have local boxicity $O(\Delta)$, while almost all graphs of maximum degree $\Delta$ have local boxicity $\Omega(\Delta)$, improving known upper and lower bounds. We ...
maximum degree $${\Delta < \lfloor{\frac{n(\alpha-1)}{2\alpha}}\rfloor}$$ for some $${\alpha \in \mathbb{N}_{\geq 2}}$$ , then box(G) ≤ α. We also demonstrate a graph having box(G) > α ...
We show that the intersection dimension of graphs with respect to several hereditary properties can be bounded as a function of the maximum degree . As an interesting special case, we show ...
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