0
$\begingroup$

Is there a graph $G$ such that $\chi(G)$ is finite, but there is no total coloring with finitely many colours?

$\endgroup$

1 Answer 1

2
$\begingroup$

Yes there is: consider the complete bipartite graph $K_{\omega,\omega}$, which has chromatic number 2, but every total coloring requires infinitely many colors.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.