Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes occurring among the vertices, taken over all proper edge-colorings of the multigraph itself. In this framework, the palette pseudograph of an edge-colored multigraph is defined in this paper and some of its properties are investigated. We show that these properties can be applied in a natural way in order to produce the first known family of multigraphs whose palette index is expressed in terms of the maximum degree by a quadratic polynomial. We also attempt an analysis of our result in connection with some related questions.
Titolo: | A family of multigraphs with large palette index |
Autori: | Mazzuoccolo, Giuseppe (Corresponding) |
Data di pubblicazione: | 2019 |
Rivista: | |
Handle: | http://hdl.handle.net/11562/1010418 |
Appare nelle tipologie: | 01.01 Articolo in Rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
abm_revision_submitted11032019.pdf | Documento in Pre-print | Accesso ristretto | Open Access Visualizza/Apri |