- Tytuł:
- Acyclic 6-Colouring of Graphs with Maximum Degree 5 and Small Maximum Average Degree
- Autorzy:
- Fiedorowicz, Anna
- Powiązania:
- https://bibliotekanauki.pl/articles/30146851.pdf
- Data publikacji:
- 2013-03-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
acyclic colouring
bounded degree graph
maximum average degree - Opis:
- A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . ., k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, every cycle in G has at least three distinct colours. Acyclic colourings were introduced by Gr¨unbaum in 1973, and since then have been widely studied. In particular, the problem of acyclic colourings of graphs with bounded maximum degree has been investigated. In 2011, Kostochka and Stocker showed that any graph with maximum degree 5 can be acyclically coloured with at most 7 colours. The question, whether this bound is achieved, remains open. In this note we prove that any graph with maximum degree 5 and maximum average degree at most 4 admits an acyclic 6-colouring. We also provide examples of graphs with these properties.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 91-99
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł