The extremal functions for triangle-free graphs with excluded minors

Robin Thomas; Youngho Yoo

The extremal functions for triangle-free graphs with excluded minors

Combinatorics 2018-07-18 v2

Authors: Robin Thomas , Youngho Yoo

Abstract

We prove two results: 1. A graph $G$ on at least seven vertices with a vertex $v$ such that $G-v$ is planar and $t$ triangles satisfies $|E(G)| \leq 3|V(G)|- 9 + t/3$ . 2. For $p=2,3,\ldots,9$ , a triangle-free graph $G$ on at least $2p-5$ vertices with no $K_p$ -minor satisfies $|E(G)|\leq (p-2)|V(G)| - (p-2)^2$ .

Keywords

graph pebbling graph theory

Cite

@article{arxiv.1801.06887,
  title  = {The extremal functions for triangle-free graphs with excluded minors},
  author = {Robin Thomas and Youngho Yoo},
  journal= {arXiv preprint arXiv:1801.06887},
  year   = {2018}
}

Comments

12 pages, no figures. Revised according to referees' comments

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