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Planar Turán number of quasi-double stars

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  • Liu, Huiqing
  • Xie, Tian
  • Zhao, Qin

Abstract

Given a graph H, we call a graph H-free if it does not contain H as a subgraph. The planar Turán number of a graph H, denoted by exP(n,H), is the maximum number of edges in a planar H-free graph on n vertices. A (h, k)-quasi-double star Wh,k, obtained from a path P3=v1v2v3 by adding h leaves and k leaves to the vertices v1 and v3, respectively, is a subclass of caterpillars. In this paper, we study exP(n,Wh,k) for all 1 ≤ h ≤ 2 ≤ k ≤ 5, and obtain that exP(n,Wh,k)=3(h+k)h+k+2n for 3≤h+k≤5 and exP(n,W1,5)=52n. Furthermore, we establish that 94n≤exP(n,W2,4)≤52n and 52n≤exP(n,W2,5)≤176n.

Suggested Citation

  • Liu, Huiqing & Xie, Tian & Zhao, Qin, 2026. "Planar Turán number of quasi-double stars," Applied Mathematics and Computation, Elsevier, vol. 526(C).
    • Handle: RePEc:eee:apmaco:v:526:y:2026:i:c:s0096300326001396
    DOI: 10.1016/j.amc.2026.130087
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