Submit progress

on Erdős #1111 · graph theory

The statement

If $G$ is a finite graph and $A,B$ are disjoint sets of vertices then we call $A,B$ anticomplete if there are no edges between $A$ and $B$ .

If $t,c\geq 1$ then there exists $d\geq 1$ such that if $\chi(G)\geq d$ and $\omega(G)<t$ then there are anticomplete sets $A,B$ with $\chi(A)\geq \chi(B)\geq c$ .

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.