Polychromatic colorings of complete graphs with respect to 1‐, 2‐factors and Hamiltonian cycles

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2018-04-01
Authors
Axenovich, Maria
Lidicky, Bernard
Goldwasser, John
Hansen, Ryan
Lidicky, Bernard
Martin, Ryan
Offner, David
Talbot, John
Young, Michael
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Abstract

If G is a graph and H is a set of subgraphs of G, then an edge-coloring of G is called H-polychromatic if every graph from H gets all colors present in G on its edges. The H-polychromatic number of G, denoted polyH(G), is the largest number of colors in an H-polychromatic coloring. In this paper, polyH(G) is determined exactly when G is a complete graph and H is the family of all 1-factors. In addition polyH(G) is found up to an additive constant term when G is a complete graph and H is the family of all 2-factors, or the family of all Hamiltonian cycles.

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<p>This is the peer reviewed version of the following article: Axenovich M, Goldwasser J, Hansen R, Lidický B, Martin RR, Offner D, Talbot J, Young M. Polychromatic colorings of complete graphs with respect to 1-, 2-factors and Hamiltonian cycles. J Graph Theory. 2018;87:660–671, which has been published in final form at doi: <a href="https://doi-org.proxy.lib.iastate.edu/10.1002/jgt.22180">10.1002/jgt.22180</a>. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.</p>
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