Concepedia

On the linear vertex‐arboricity of a planar graph

K. S. Poh

Journal of Graph Theory · 1990 · 82 citations · 6 references

DOI

Concepts

Abstract

Abstract We prove in this note that the linear vertex‐arboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others.

References

6

Defective colorings of graphs in surfaces: Partitions into subgraphs of bounded valency

Lenore Cowen, Robert Cowen, Douglas R. Woodall · Journal of Graph Theory · 1986 · 279 citations

, , +8

The Point-Arboricity of Planar Graphs

Gary Chartrand, Hudson V. Kronk · Journal of the London Mathematical Society · 1969 · 139 citations · Full text

, , +9

The point-arboricity of a graph

Gary Chartrand, Hudson V. Kronk, Curtiss E. Wall · Israel Journal of Mathematics · 1968 · 122 citations

, , +8

A generalization of the chromatic number

Gary Chartrand, Dennis P. Geller, Stephen T. Hedetniemi · Mathematical Proceedings of the Cambridge Philosophical Society · 1968 · 74 citations

, , +5

Path chromatic numbers of graphs

Jin Akiyama, Hiroshi Era, Severino V. Gervacio et al. · Journal of Graph Theory · 1989 · 20 citations

, , +9