An extension of a result concerning convex geometric graphs

TL;DR

This paper proves a general result related to the Erdős–Sós Conjecture, establishing conditions under which a graph contains every tree of a certain size as a subgraph, advancing understanding in convex geometric graph theory.

Contribution

It extends a known result by proving the Erdős–Sós Conjecture for a broader class of graphs, specifically in the context of convex geometric graphs.

Findings

Proves the Erdős–Sós Conjecture under new conditions

Demonstrates that graphs with more than half of (k-1)n edges contain all trees of order k+1

Advances theoretical understanding of subgraph containment in convex geometric graphs

Abstract

We show a general result known as the Erdos_Sos Conjecture: if $E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of order $k+1$ as a subgraph.