Four-colorings of maximal outerplanar graphs under boundary conditions. (Chinese. English summary) Zbl 0959.05053

Xie, Litong; Liu, Guizhen

Acta Math. Appl. Sin. 21, No. 1, 135-138 (1998).

Summary: Four colourings of maximum outerplanar graphs are studied by their diagonal transformations and the concept of a characteristic vector is given. It is proved that for any two maximum outerplanar graphs with a common boundary circuit, one can be obtained from the other by a series of diagonal transformations. Furthermore, it is proved that under some conditions two maximum outerplanar graphs with a common boundary circuit have common four colourings.

MSC:

05C15

Coloring of graphs and hypergraphs

Keywords:

maximum outerplanar graphs; diagonal transformations; four colourings