منابع مشابه
Acyclic colourings of graphs with bounded degree
In 1999 Boiron et al. conjectured that a graph G with maximum degree at most 3 has an acyclic 2-colouring such that the set of vertices in each colour induces a subgraph with maximum degree at most 2. In this paper we prove this conjecture and show that such a colouring of a cubic graph can be determined in polynomial time. We also prove that it is an NP-complete problem to decide if a graph wi...
متن کاملAcyclic improper colourings of graphs with bounded maximum degree
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour classes is acyclic and each colour class induces a graph with maximum degree at most t. We consider the supremum, over all graphs of maximum degree at most d, of the acyclic t-improper chromatic number and provide t-impr...
متن کاملAcyclic improper colourings of graphs with bounded degree
In this paper, we continue the study of acyclic improper colourings of graphs introduced in a previous work. An improper colouring of a graph G is a mapping c from the set of vertices of G to a set of colours such that for every colour i, the subgraph induced by the vertices with colour i satisses some property depending on i. Such an improper colouring is acyclic if for every two distinct colo...
متن کاملAcyclic T -improper Colourings of Graphs with Bounded Maximum Degree
For graphs of bounded maximum degree, we consider acyclic t-improper colourings, that is, colourings in which each bipartite subgraph consisting of the edges between two colour classes is acyclic and each colour class induces a graph with maximum degree at most t. In the first part, we show that all subcubic graphs are acyclically 1-improperly 3-choosable, thus extending a result of Boiron, Sop...
متن کاملk-forested choosability of graphs with bounded maximum average degree
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2018
ISSN: 1571-0653
DOI: 10.1016/j.endm.2018.06.029