Exoo-Ismailescu-Lim Graphs
The Exoo-Ismailescu-Lim graphs are a set of high-chromatic number graphs with graph dimension 4 as summarized in the following table.
Note that the paper defining these graphs (Exoo et al. 2014) unfortunately contained two errors of sign and one of permutation. In the construction of the 14-vertex graph (called G in the paper), the first coordinate of v_(14) (line -6 on page 419) should read 1+sqrt(5) rather than 1-sqrt(5). In addition, the edges given at the top of page 420 give a graph isomorphic to the one constructed on the given vertices but using a permuted set of vertices. Finally, in the construction of the 65-vertex graph (called K in the paper), the entry in row 5, column 1 of Table 2 on page 422 should read 1-sqrt(5) rather than 1+sqrt(5).
The Exoo-Ismailescu graphs (as corrected above) will be implemented in a future version of the Wolfram Language as GraphData ["ExooIsmailescuLimGraph14"] etc.
See also
Exoo-Ismailescu Graphs, Graph Dimension, Unit-Distance GraphExplore with Wolfram|Alpha
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References
Exoo, G.; Ismailescu, D.; and Lim, M. "On the Chromatic Number of R^4." Disc. Comput. Geom. 52, 416-423, 2014.Cite this as:
Weisstein, Eric W. "Exoo-Ismailescu-Lim Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Exoo-Ismailescu-LimGraphs.html