3 problems

For integers $n$ and $c$, let $f(n,c)$ be the least integer $d$ such that every $n$-vertex graph with minimum degree at least $d$ contains a cycle with at least $c$ chords. Kára an…

All graphs are finite and simple. A graph is $k$-critical if its chromatic number is $k$ and every proper subgraph is $(k-1)$-colorable. Let $g_k(n)$ be the largest integer…

A graph is finite and simple, and the minimum degree of a graph is the least degree among its vertices. Kára and Král's conjecture. Every graph on $31$ vertices with minimum degree…