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\iteman{io-port 05992344}
\itemau{van Kreveld, Marc}
\itemti{Bold graph drawings.}
\itemso{Comput. Geom. 44, No. 9, 499-506 (2011).}
\itemab
Summary: When a graph is drawn in a classical manner, its vertices are shown as small disks and its edges with a positive width; zero-width edges and zero-size vertices exist only in theory. Let $r$ denote the radius of the disks that show vertices and $w$ the width of edges. We give a list of conditions that make such a drawing good and that apply to not necessarily planar graphs. We show that if $r<w$, a vertex must have constant degree for a drawing to satisfy the conditions, and if $r\geqslant w$, a vertex can have any degree. We also give an algorithm that, for a given drawing and values for $r$ and $w$, determines whether the bold drawing satisfies the conditions. Furthermore, we show how to maximize $r$ and/or $w$ without violating the conditions in polynomial time.
\itemrv{~}
\itemcc{}
\itemut{graph drawing; edge and vertex size; planar straight-line drawing}
\itemli{doi:10.1016/j.comgeo.2011.06.002}
\end