Some maximum multigraphs and adge/vertex distance colourings
نویسنده
چکیده
Shannon–Vizing–type problems concerning the upper bound for a distance chromatic index of multigraphs G in terms of the maximum degree ∆(G) are studied. Conjectures generalizing those related to the strong chromatic index are presented. The chromatic d–index and chromatic d–number of paths, cycles, trees and some hypercubes are determined. Among hypercubes, however, the exact order of their growth is found.
منابع مشابه
Partitions and Edge Colourings of Multigraphs
Erdős and Lovász conjectured in 1968 that for every graph G with χ(G) > ω(G) and any two integers s, t ≥ 2 with s+ t = χ(G)+1, there is a partition (S, T ) of the vertex set V (G) such that χ(G[S]) ≥ s and χ(G[T ]) ≥ t. Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for line graphs of multigraphs.
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 15 شماره
صفحات -
تاریخ انتشار 1995