ChromaticNumber on LabeledGraph
The fewest colors for the vertices so that adjacent vertices differ.
FindStat's St000098. The colorings in k colors are counted as the covers of the vertices by k independent sets, Σ over the subsets S of (-1)^(n - |S|) i(S)^k with i(S) the independent sets inside S, and the number is the least k with one. The graph with no vertices gives 0.
Called as CombinatorialStat(x, "ChromaticNumber"). The head's page has its examples.
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Distribution
Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000098
The chromatic number of a graph.
| Object | Value |
|---|---|
([],0) | 0 |
([],1) | 1 |
([],2) | 1 |
([],3) | 1 |
([],4) | 1 |
([],5) | 1 |
([],6) | 1 |
([],7) | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000098 has the rest.