A disproof of a gap-one conjecture for the equitable chromatic number of block graphs

Juho Lauri

For a graph $G$, let $L(G)=\max \{\omega (G),\lceil (|V(G)|+1)/({\alpha }_{\min }(G)+1)\rceil \}$, where $\omega (G)$ is the clique number and ${\alpha }_{\min }(G)$ is the minimum, over all vertices $v$, of the…