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geometric graph
Circular colouring the orthogonality graph ★★
Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr
Let denote the graph with vertex set consisting of all lines through the origin in
and two vertices adjacent in
if they are perpendicular.
Problem Is
?
![$ \chi_c({\mathcal O}) = 4 $](/files/tex/ee0ecd597af84da66753671f734858c77288d4be.png)
Keywords: circular coloring; geometric graph; orthogonality
Coloring the Odd Distance Graph ★★★
Author(s): Rosenfeld
The Odd Distance Graph, denoted , is the graph with vertex set
and two points adjacent if the distance between them is an odd integer.
Question Is
?
![$ \chi({\mathcal O}) = \infty $](/files/tex/cb1eb2f7a7c0eacc877dca7708d0e44b2835f0c2.png)
Keywords: coloring; geometric graph; odd distance
Universal point sets for planar graphs ★★★
Author(s): Mohar
We say that a set is
-universal if every
vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in
, and all edges are (non-intersecting) straight line segments.
Question Does there exist an
-universal set of size
?
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ O(n) $](/files/tex/ee18510ab4140627d7a8df7949d309533b39ebca.png)
Keywords: geometric graph; planar graph; universal set
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