Journal or Book Title
Journal of Graph Theory
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.
Wiley Periodicals, Inc.
Axenovich, Maria; Goldwasser, John; Hansen, Ryan; Lidicky, Bernard; Martin, Ryan R.; Offner, David; Talbot, John; and Young, Michael, "Polychromatic colorings of complete graphs with respect to 1‐, 2‐factors and Hamiltonian cycles" (2018). Mathematics Publications. 188.