We consider the colorings of the edges of a multigraph in such a way that every nonpendant vertex is incident to at least two edges of the same color. The maximum number of colors that can be used in such colorings is the upper chromatic index of a multigraph G, denoted by \bar(\chi)'(G). We prove that if a multigraph G has n vertices, m edges, p pendant vertices and maximum number c disjoint cycles, then \bar(\chi)'(G) = c + m - n + p.
On the upper chromatic index of a multigraph
GIONFRIDDO, Mario;MILAZZO, Lorenzo Maria Filippo;
2002-01-01
Abstract
We consider the colorings of the edges of a multigraph in such a way that every nonpendant vertex is incident to at least two edges of the same color. The maximum number of colors that can be used in such colorings is the upper chromatic index of a multigraph G, denoted by \bar(\chi)'(G). We prove that if a multigraph G has n vertices, m edges, p pendant vertices and maximum number c disjoint cycles, then \bar(\chi)'(G) = c + m - n + p.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
