# Minor stars in plane graphs with minimum degree five

## TL;DR

This paper characterizes minor 5-stars in plane graphs with minimum degree five, extending previous work and providing new insights into their weight and height properties.

## Contribution

It offers two new descriptions of minor 5-stars in such graphs, enabling the extension of existing results and the derivation of new properties.

## Key findings

- Descriptions of minor 5-stars in plane graphs with minimum degree five
- Extended results on weight and height of subgraphs in these graphs
- New theoretical insights into the structure of plane graphs with degree constraints

## Abstract

The weight of a subgraph $H$ in $G$ is the sum of the degrees in $G$ of vertices of $H$. The {\em height} of a subgraph $H$ in $G$ is the maximum degree of vertices of $H$ in $G$. A star in a given graph is minor if its center has degree at most five in the given graph. Lebesgue (1940) gave an approximate description of minor $5$-stars in the class of normal plane maps with minimum degree five. In this paper, we give two descriptions of minor $5$-stars in plane graphs with minimum degree five. By these descriptions, we can extend several results and give some new results on the weight and height for some special plane graphs with minimum degree five.