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- W2003268018 abstract "A triangle incident with vertices of degrees a, b and c is said to be an (a, b, c)-triangle. We prove that every plane triangulation contains an (a, b, c)-triangle where (a, b, c) ϵ {(3, 4, c), 4 ⩽ c ⩽ 35; (3, 5, c), 5 ⩽ c ⩽ 21; (3, 6, c), 6 ⩽ c ⩽ 20; (3, 7, c), 7 ⩽ c ⩽ 16; (3, 8, c), 8 ⩽ c ⩽ 14; (3, 9, c), 9 ⩽ c ⩽ 14; (3, 10, c), 10 ⩽ c ⩽ 13; (4, 4, c), c ⩾ 4; (4, 5, c), 5 ⩽ c ⩽ 13; (4, 6, c), 6 ⩽ c ⩽ 17; (4, 7, c), 7 ⩽ c ⩽ 8; (5, 5, c), 5 ⩽ c ⩽ 7; (5, 6, 6)}. Moreover, we provide lower bounds for the maximum values c in all cases mentioned above. This result strengthens classical results by Lebesgue and Kotzig and a recent result by Borodin." @default.
- W2003268018 created "2016-06-24" @default.
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- W2003268018 date "1999-02-01" @default.
- W2003268018 modified "2023-09-28" @default.
- W2003268018 title "Triangles with restricted degrees of their boundary vertices in plane triangulations" @default.
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- W2003268018 doi "https://doi.org/10.1016/s0012-365x(98)00172-1" @default.
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