Chromatic Spectrum of Ks-WORM Colorings of Kn

Allagan Julian-A.; Jones Kenneth L.

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2023-02-19 12:33

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519.17/.179 (1)

Analiză combinatorică. Teoria grafurilor (115)

SM ISO690:2012

ALLAGAN, Julian-A., JONES, Kenneth L.. Chromatic Spectrum of Ks-WORM Colorings of Kn. In: Computer Science Journal of Moldova, 2020, nr. 2(83), pp. 170-186. ISSN 1561-4042.

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Computer Science Journal of Moldova

Numărul 2(83) / 2020 / ISSN 1561-4042 /ISSNe 2587-4330

Chromatic Spectrum of Ks-WORM Colorings of K_n

CZU: 519.17/.179

MSC 2010: 05C15, 05C30, 05C35, 05C65.

Pag. 170-186

Allagan Julian-A., Jones Kenneth L.

Elizabeth City State University

Disponibil în IBN: 14 septembrie 2020

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Rezumat

An H-WORM coloring of a simple graph G is the coloring of the vertices of G such that no copy of H b G is monochrome or rainbow. In a recently published article by one of the authors [3], it was claimed that the number of r-partitions in a Ks-WORM coloring of Kn is C_n r, where n r denotes the Stirling number of the second kind, for all 3 B r B s n. We found that C_n r if and only if n3 2 s B n with r s. Further investigations into 2, given any K3-WORM coloring of Kn, show its relation with the number of spanning trees of cacti and the Catalan numbers. Moreover, we extend the notion of H-WORM colorings to H1;H2-mixed colorings, where H1 and H2 are distinct subgraphs of G; these coloring constraints are closely related to those of mixed hypergraph colorings.

Cuvinte-cheie
Catalan numbers, Chromatic spectrum, Mixed hypergraph coloring, Stirling numbers

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<dc:creator>Jones, K.</dc:creator>
<dc:date>2020-09-11</dc:date>
<dc:description xml:lang='en'><p>An H-WORM coloring of a simple graph G is the coloring of the vertices of G such that no copy of H b G is monochrome or rainbow. In a recently published article by one of the authors [3], it was claimed that the number of r-partitions in a Ks-WORM coloring of Kn is C<sub>n</sub> r, where n r denotes the Stirling number of the second kind, for all 3 B r B s n. We found that C<sub>n</sub> r if and only if n3 2  s B n with r s. Further investigations into 2, given any K3-WORM coloring of Kn, show its relation with the number of spanning trees of cacti and the Catalan numbers. Moreover, we extend the notion of H-WORM colorings to H1;H2-mixed colorings, where H1 and H2 are distinct subgraphs of G; these coloring constraints are closely related to those of mixed hypergraph colorings.</p></dc:description>
<dc:source>Computer Science Journal of Moldova 83 (2) 170-186</dc:source>
<dc:subject>Catalan numbers</dc:subject>
<dc:subject>Chromatic spectrum</dc:subject>
<dc:subject>Mixed
hypergraph coloring</dc:subject>
<dc:subject>Stirling numbers</dc:subject>
<dc:title>Chromatic Spectrum of Ks-WORM Colorings of Kn</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
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