F-WORM colorings of some 2-trees: partition vectors

ECSU Author/Contributor (non-ECSU co-authors, if there are any, appear on document)
Julian A. D. Allagan , Associate Professor (Creator)
Elizabeth City State University (ECSU )
Web Site: https://www.ecsu.edu/academics/library/index.html

Abstract: A collection of distinct subgraphs of a graphG = (V;E).An F-WORM coloring of G is the coloring of its vertices such that no copy of each subgraphFi 2 F is monochrome or rainbow. This generalizes the notion of F-WORMcoloring that was introduced recently by W. Goddard, K. Wash, and H. Xu. A (restricted)partition vector is a sequence whose terms r are the number of F-WORMcolorings using exactly r colors, with. The partition vectors of complete graphsand those of some 2-trees are discussed. We show that, although 2-trees admit the samepartition vector in classic proper vertex colorings which forbid monochrome K2, their partition vectors in K3-WORM colorings are different.

Additional Information

Language: English
Date: 2018
2-tree, maximal outerplanar, partition, Stirling numbers.

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