A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class script T sign(5) of plane triangulations of minimum degree 5. It is known that each G ∈ script T sign(5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C4 and C5 in each G ∈ script T sign(5) follows. We prove here that each G ∈ script T sign(5) contains also light cycles C6,C7,C8 and C9 such that every vertex is of degree at most 11, 17,29 and 41, respectively. Moreover, we prove that no cycle Ck with k≥11 is light in the class script T sign(5).
|Number of pages||15|
|Publication status||Published - Feb 28 1999|
- Light subgraph
- Planar graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics