Planar Turan number of the disjoint union of cycles
DISCRETE APPLIED MATHEMATICS(2024)
摘要
The planar Turan number of H, denoted by ex(P)(n, H), is the maximum number of edges in an n-vertex H-free planar graph. The planar Turan number of k >= 3 vertex-disjoint union of cycles is a trivial value 3n - 6. Lan, Shi and Song determine the exact value of ex(P)(n, 2C(3)). We continue to study planar Turan number of two vertex-disjoint union of cycles and obtain the exact value of ex(P)(n, H), where H is vertex-disjoint union of C-3 and C-4. The extremal graphs are also characterized. We also improve the lower bound of ex(P)(n, 2C(k)) when n is sufficiently large.(c) 2023 Published by Elsevier B.V.
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关键词
Planar Turan number,Disjoint union of C-3 and C-4,Extremal graphs,Lower bound
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