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Hochberg-O'Donnell Fish Graph

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HochbergODonnellFishGraph

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance 4-chromatic graph with girth 4 listed by Soifer (2016, p. 445).

However, the Exoo-Ismailescu graphs on 17, 19, and 21 nodes are smaller.

The graph is implemented in the Wolfram Language as GraphData["HochbergODonnellFishGraph"].

See also

Braced Polygon, Exoo-Ismailescu Graphs, Fish Graph, Unit-Distance Graph

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References

Exoo, G. and Ismailescu, D. "Small Order Triangle-Free 4-Chromatic Unit Distance Graphs." Geombinatorics 26, 49-64, 2016.Hochberg, R. and O'Donnell, P. "Some 4-Chromatic Unit-Distance Graphs Without Small Cycles." Geombinatorics 5, 137-141, 1996.Soifer, A. Open Problems in Mathematics (Ed. J. F. Nash, Jr. and M. Th. Rassias). Switzerland: Springer, p. 445, 2016.Taxel, P. "Are 4-Chromatic 3-Connected Unit Distance Graphs Always Rigid?" Dec. 25, 2020. https://math.stackexchange.com/questions/3958839/are-4-chromatic-3-connected-unit-distance-graphs-always-rigid.

Cite this as:

Weisstein, Eric W. "Hochberg-O'Donnell Fish Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hochberg-ODonnellFishGraph.html

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