Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles (Q641163)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles |
scientific article; zbMATH DE number 5961708
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles |
scientific article; zbMATH DE number 5961708 |
Statements
Total colorings of planar graphs with maximum degree seven and without intersecting 3-cycles (English)
0 references
21 October 2011
0 references
The authors consider total colourings of planar graphs. The total chromatic number \(\chi''(G)\) of a graph \(G\) is the smallest integer \(k\) such that \(G\) has a total-\(k\)-colouring. The main result of the present paper is the following theorem: If a planar graph \(G\) contains no intersecting triangles and \(\Delta(G)\geq 7\), then \(\chi''(G)= \Delta(G)+ 1\).
0 references
total coloring
0 references
planar graph
0 references
0 references
0 references
