Description
A Halin graph is a planar graph consisting of a tree and an additional cycle connecting all the leaves in such manner that no two edges are crossing.
Total colouring of a graph is a mapping from the set of vertices and edges to a set of colours such that no two neighbouring objects receive the same colour.
As there were only 4 known cubic Halin graphs with total chromatic index greater than 4, a natural question of whether the number of such graphs is finite had arisen.
We managed to prove that the set of cubic Halin graphs with total chromatic index greater than 4 is finite, containing only the cubic Halin graphs known before-hand. By a slight modification of our approach, we managed to establish similar results for total and also AVD-colouring of subcubic Halin graphs.
| Pracovisko fakulty (katedra)/ Department of Faculty | Katedra informatiky |
|---|---|
| Tlač postru/ Print poster | Budem požadovať tlač /I hereby required to print the poster in faculty |
