Name
Abstract | ||
|---|---|---|
A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class T (5) of plane triangulations of minimum degree 5. It is known that each G ϵ T (5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C 4 and C 5 in each G ϵ T (5) follows. We prove here that each G ϵ T (5) contains also light cycles C 6 , C 7 , C 8 and C 9 such that every vertex is of degree at most 11, 17, 29 and 41, respectively. Moreover, we prove that no cycle C k with k ⩾ 11 is light in the class T (5) . |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1016/S0012-365X(98)00254-4 | Discrete Mathematics |
Keywords | Field | DocType |
cycles,planar graph,52b10,plane triangulations,triangulation,05c10,05c38,light cycle,light subgraph,plane graph | Discrete mathematics,Combinatorics,Loop (graph theory),Graph power,Graph factorization,Cycle graph,String graph,Regular graph,Degree (graph theory),Planar graph,Mathematics | Journal |
Volume | Issue | ISSN |
197-198, | 1-3 | Discrete Mathematics |
Citations | PageRank | References |
21 | 1.73 | 6 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stanislav Jendrol' | 1 | 283 | 38.72 |
| Tomáš Madaras | 2 | 112 | 11.15 |
| Roman Soták | 3 | 128 | 24.06 |
| Zsolt Tuza | 4 | 1889 | 262.52 |