Improper colourings inspired by Hadwiger's conjecture
نویسندگان
چکیده
منابع مشابه
On monochromatic component size for improper colourings
This paper concerns improper λ-colourings of graphs and focuses on the sizes of the monochromatic components (i.e., components of the subgraphs induced by the colour classes). Consider the following three simple operations, which should, heuristically, help reduce monochromatic component size: (a) assign to a vertex the colour that is least popular among its neighbours; (b) change the colours o...
متن کاملImproper Colourings of Unit Disk Graphs
We investigate the following problem proposed by Alcatel. A satellite sends information to receivers on earth, each of which is listening on a chosen frequency. Technically, it is impossible for the satellite to precisely focus its signal onto a receiver. Part of the signal will be spread in an area around its destination and this creates noise for nearby receivers on the same frequency. Howeve...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2018
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms.12127