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Correspondence Chromatic Number


The correspondence chromatic number chi_(DP)(G) of a finite simple graph G with at least one graph vertex is the least positive integer k such that every assignment of pairwise disjoint finite sets of at least k colors to its vertices, with a matching between the color sets at the endpoints of each edge, admits a correspondence coloring (Dvorák and Postle 2018). It is also called the DP chromatic number.

For such a graph with maximum vertex degree Delta, this number is at most Delta+1, since each previously colored adjacent vertex forbids at most one color in a successive coloring. It is at least the choice number, since ordinary list coloring is a special case of correspondence coloring.


See also

Choice Number, Chromatic Number, Correspondence Coloring

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References

Dvorák, Z. and Postle, L. "Correspondence Coloring and Its Application to List-Coloring Planar Graphs Without Cycles of Lengths 4 to 8." J. Combin. Th. Ser. B 129, 38-54, 2018. https://doi.org/10.1016/j.jctb.2017.09.001.

Cite this as:

Weisstein, Eric W. "Correspondence Chromatic Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CorrespondenceChromaticNumber.html

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