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Exoo-Ismailescu-Lim Graphs


Exoo-Ismailescu-LimGraphs

The Exoo-Ismailescu-Lim graphs are a set of high-chromatic number graphs with graph dimension 4 as summarized in the following table.

nchiname
14714-Exoo-Ismailescu-Lim graph
26826-Exoo-Ismailescu-Lim graph
65965-Exoo-Ismailescu-Lim graph

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 Graph

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References

Exoo, G.; Ismailescu, D.; and Lim, M. "On the Chromatic Number of R^4." Disc. Comput. Geom. 52,Ê416-423, 2014.

Cite this as:

Weisstein, Eric W. "Exoo-Ismailescu-Lim Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Exoo-Ismailescu-LimGraphs.html

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