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- W2963041596 abstract "Abstract 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 ) | ≥ 2 n + 4 5 . For a cubic essentially 4-connected planar graph G, Grunbaum with Malkevitch, and Zhang showed that G has a cycle on at least 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." @default.
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- W2963041596 date "2016-11-01" @default.
- W2963041596 modified "2023-09-30" @default.
- W2963041596 title "On Longest Cycles in Essentially 4-connected Planar Graphs" @default.
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- W2963041596 doi "https://doi.org/10.1016/j.endm.2016.10.036" @default.
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