On (p,1)-total labelling of plane graphs with independent crossings
نویسندگان
چکیده
منابع مشابه
Coloring plane graphs with independent crossings
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether graphs drawn in the plane with all crossings independent are 5-colorable.
متن کاملThe structure of plane graphs with independent crossings and its applications to coloring problems
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is ∆ if ∆ ≥ 8, the list edge ...
متن کاملDrawing complete multipartite graphs on the plane with restrictions on crossings
We introduce the concept of NIC-planar graphs and present the full characterization of NIC-planar complete k-partite graphs.
متن کاملColoring graphs with crossings
We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three crossings, but does not contain K6 as a subgraph, then it is also 5-colorable. We also consider the question of whether the result can be extended to graphs with more crossings.
متن کاملTotal-colouring of plane graphs with maximum degree nine
The central problem of the total-colourings is the Total-Colouring Conjecture, which asserts that every graph of maximum degree ∆ admits a (∆ + 2)-total-colouring. Similarly to edge-colourings—with Vizing’s edge-colouring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degree. More precisely, it is known that if ∆ ≥ 10 then every plane graph of maximum degree ∆ is...
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ژورنال
عنوان ژورنال: Filomat
سال: 2012
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1206091z