# On Convex Graphs Having Plane Spanning Subgraph of Certain Type

## TL;DR

This paper investigates the conditions under which the complete graph minus a certain subgraph admits a g-angulation, providing necessary and sufficient criteria for various sizes of the subgraph.

## Contribution

It establishes new necessary and sufficient conditions for the existence of g-angulations in graphs formed by removing specific subgraphs from complete graphs.

## Key findings

- Characterization of subgraphs F with |E(F)| ≤ n-1 for g-angulation
- Conditions for placing F in K_n when |E(F)| ≥ n to achieve g-angulation
- Extension of previous results to broader classes of subgraphs

## Abstract

Motivated by a result of [17], we determine necessary and sufficient conditions on $F\/$ with $|E(F)| \leq n-1\/$ for which $K_n - F\/$ admits a $g$-angulation. For $|E(F)| \geq n\/$, we investigate the possibility of placing $F\/$ in $K_n\/$ such that $K_n -F\/$ admits a $g$-angulation for certain families of graphs $F\/$.