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- W2030327493 abstract "A defining set (of vertex coloring) of a graph G is a set of vertices S with an assignment of colors to its elements which has a unique completion to a proper coloring of G. We define a minimal defining set to be a defining set which does not properly contain another defining set. If G is a uniquely vertex colorable graph, clearly its minimum defining sets are of size χ(G)−1. It is shown that for a coloring of G, if all minimal defining sets of G are of size χ(G)−1, then G is a uniquely vertex colorable graph." @default.
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- W2030327493 date "1999-03-01" @default.
- W2030327493 modified "2023-09-27" @default.
- W2030327493 title "A characterization of uniquely vertex colorable graphs using minimal defining sets" @default.
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- W2030327493 doi "https://doi.org/10.1016/s0012-365x(98)00304-5" @default.
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