A counterexample to the $S_{10}$- and the $S_{12}$-Conjecture

Isaak H. Wolf

For two graphs $G$ and $H$, a mapping $f:E(G)\to E(H)$ is an $H$-coloring of $G$, if it is a proper edge-coloring and for every $v\in V(G)$ there exists a vertex $u \in V(H…