Graphs and Combinatorics

, Volume 32, Issue 3, pp 923–942 | Cite as

Counting Carambolas

  • Adrian Dumitrescu
  • Maarten Löffler
  • André Schulz
  • Csaba D. TóthEmail author
Original Paper


We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of n points in the plane. Configurations of interest include convex polygons, star-shaped polygons and monotone paths. We also consider related problems for directed planar straight-line graphs.


Convex polygon Star-shaped polygon Monotone path  Plane graph Triangulation Counting 



A. Dumitrescu was supported in part by NSF grant DMS-1001667. M. Löffler was supported by the Netherlands Organization for Scientific Research (NWO) under grant 639.021.123. Research by Tóth was supported in part by NSERC (RGPIN 35586) and NSF (CCF-1423615). This work was initiated at the workshop “Counting and Enumerating Plane Graphs,” which took place at Schloss Dagstuhl in March, 2013.


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Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Adrian Dumitrescu
    • 1
  • Maarten Löffler
    • 2
  • André Schulz
    • 3
  • Csaba D. Tóth
    • 4
    • 5
    Email author
  1. 1.Department of Computer ScienceUniversity of Wisconsin-MilwaukeeMilwaukeeUSA
  2. 2.Department of Computing and Information SciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.LG Theoretische InformatikFernUniversität HagenHagenGermany
  4. 4.Department of MathematicsCalifornia State University NorthridgeLos AngelesUSA
  5. 5.Department of Computer ScienceTufts UniversityMedfordUSA

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