- Tytuł:
- On Longest Cycles in Essentially 4-Connected Planar Graphs
- Autorzy:
-
Fabrici, Igor
Harant, Jochen
Jendroľ, Stanislav - Tematy:
-
planar graph
longest cycle - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/31340878.pdf Link otwiera się w nowym oknie
- Opis:
- A planar 3-connected graph $ G $ is essentially 4-connected if, for any 3-separator $ S $ of $ G $, one component of the graph obtained from $ G $ by removing $ S $ is a single vertex. Jackson and Wormald proved that an essentially 4-connected planar graph on n vertices contains a cycle $ C $ such that $ |V(C)| \ge \frac{2n+4}{5} $. For a cubic essentially 4-connected planar graph $G$, Grünbaum with Malkevitch, and Zhang showed that $G$ has a cycle on at least $ \frac{3}{4} n $ vertices. In the present paper the result of Jackson and Wormald is improved. Moreover, new lower bounds on the length of a longest cycle of $G$ are presented if $G$ is an essentially 4-connected planar graph of maximum degree 4 or $G$ is an essentially 4-connected maximal planar graph.
- Dostawca treści:
- Biblioteka Nauki
Artykuł