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On \(J\)-colorability of certain derived graph classes. (English) Zbl 1439.05084

Summary: A vertex \(v\) of a given graph \(G\) is said to be in a rainbow neighbourhood of \(G\), with respect to a proper coloring \(\mathcal{C}\) of \(G\), if the closed neighbourhood \(N[v]\) of the vertex \(v\) consists of at least one vertex from every color class of \(G\) with respect to \(\mathcal{C}\). A maximal proper coloring of a graph \(G\) is a \(J\)-coloring of \(G\) such that every vertex of \(G\) belongs to a rainbow neighbourhood of \(G\). In this paper, we study certain parameters related to \(J\)-coloring of certain Mycielski-type graphs.

MSC:

05C15 Coloring of graphs and hypergraphs
05C38 Paths and cycles
05C75 Structural characterization of families of graphs
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References:

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