# Minors

## Highly connected graphs with no K_n minor ★★★

Author(s): Thomas

**Problem**Is it true for all , that every sufficiently large -connected graph without a minor has a set of vertices whose deletion results in a planar graph?

Keywords: connectivity; minor

## Seagull problem ★★★

Author(s): Seymour

**Conjecture**Every vertex graph with no independent set of size has a complete graph on vertices as a minor.

Keywords: coloring; complete graph; minor

## Forcing a $K_6$-minor ★★

Author(s): Barát ; Joret; Wood

**Conjecture**Every graph with minimum degree at least 7 contains a -minor.

**Conjecture**Every 7-connected graph contains a -minor.

Keywords: connectivity; graph minors

## Forcing a 2-regular minor ★★

**Conjecture**Every graph with average degree at least contains every 2-regular graph on vertices as a minor.

Keywords: minors