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Plummer-Toft Graph


Let q be the maximum face degree of a graph and chi_c its cyclic chromatic number. It is conjectured that chi_c<=q+2 for polyhedral graphs (Plummer and Toft 1987).

PlummerToftGraphs

A number of infinite families satisfying chi_c=q+2 are known, including the stacked 3-prism graphs and two other families noted by Plummer and Toft (1987). The first of these are known in this work as Plummer-Toft graphs, the first few of which are illustrated above.


See also

Cyclic Chromatic Number

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References

Plummer, M. D. and Toft, B. "Cyclic Coloration of 3-Polytopes." J. Graph Th. 11, 507-515, 1987.

Cite this as:

Weisstein, Eric W. "Plummer-Toft Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Plummer-ToftGraph.html

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