Publication at Faculty of Mathematics and Physics |
2007
Abstract
If $G$ and $H$ are graphs, then a map $\phi:\,E(G)\to E(H)$ is cycle-continuous if the pre-image of every cycle of $H$ is a cycle of $G$. Cycle-continuous maps give rise to a natural quasi-order on the class of finite graphs.
In the paper, some basic structural properties of this (and other related) quasi-orders are established. For instance, it is shown that this quasi-order has antichains of arbitratily large finite size.