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The $10$-cycle $C10$ is light in the family of all plane triangulations with minimum degree five

In: Tatra Mountains Mathematical Publications, vol. 18, no. 4
Tomáš Madaras - Roman Soták
Detaily:
Rok, strany: 1999, 35 - 56
O článku:
A subgraph of a plane graph is light if each of its vertices has a small degree in entire graph. Consider the class $T (5)$ of all plane triangulations of minimum degree $5$. It is known that each $G \in T (5)$ contains a light triangle. From a recent result of Jendroľ and Madaras, the existence of light cycles $C4$ and $C5$ in each $G \in T (5)$ follows. Jendroµ et al. proved that each $G \in T (5)$ contains light cycles $C6, C7, C8$ and $C9$, and that no cycle $Ck$ with $k≥ 11$ is light in the class $T(5)$. In this paper we supplement the above mentioned results by proving that each $G \in T (5)$ also contains a light cycle $C10$ such that every its vertex is of degree at most $415$. So the characterization of all light cycles in $T (5)$ is complete.
Ako citovať:
ISO 690:
Madaras, T., Soták, R. 1999. The $10$-cycle $C10$ is light in the family of all plane triangulations with minimum degree five. In Tatra Mountains Mathematical Publications, vol. 18, no.4, pp. 35-56. 1210-3195.

APA:
Madaras, T., Soták, R. (1999). The $10$-cycle $C10$ is light in the family of all plane triangulations with minimum degree five. Tatra Mountains Mathematical Publications, 18(4), 35-56. 1210-3195.