2022/12/24 by Ping Li, Li, Ping
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2212.12751
openalex publication_date 2022/12/24 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
The \em planar Turán number of H, denoted by exP(n,H), is the maximum number of edges in an H-free planar graph. The planar Turán number of k≥ 3 vertex-disjoint union of cycles is a trivial value 3n-6. Lan, Shi and Song determine the exact value of exP(n,2C3). We continue to study planar Turán number of vertex-disjoint union of cycles and obtain the exact value of exP(n,H), where H is vertex-disjoint union of C3 and C4. The extremal graphs are also characterized. We also improve the lower bound of exP(n,2Ck) when k is sufficiently large.