The Extremal Function for Apex Graphs

Elena Pavelescu

The Extremal Function for Apex Graphs

Combinatorics 2022-04-20 v2 Geometric Topology

Authors: Elena Pavelescu

Abstract

McCarty and Thomas conjectured that a linklessly embeddable graph with $n\ge 7$ vertices and $t$ triangles has at most $3n-9 +\frac{t}{3}$ edges. Thomas and Yoo proved this to be true for apex graphs. We give a shorter and simpler proof for the apex case.

Keywords

graph theory graph cycles graph pebbling

Cite

@article{arxiv.2204.07168,
  title  = {The Extremal Function for Apex Graphs},
  author = {Elena Pavelescu},
  journal= {arXiv preprint arXiv:2204.07168},
  year   = {2022}
}

Comments

3 pages; the proof was modified to include the non-face triangles of the planar graph H; details were added for the cases k=1 and k=2

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