in the following paper http://journal.frontiersin.org/article/10.3389/fphy.2014.00005/fullthe author describes the minimax problem as follows:Given a graph G = (V, E), we are looking for a particular coloring $C \subseteq E$ such that no two edges in $C$ share a vertex and -- and this is the part I'm confused about -- if nodes $u$ and $v$ belong to edges in $C$ then the edge (u, v) isn't in $E$.But that clearly can't make sense because somehow that means that if $(u, v) \in C$ then $(u, v) \not\in E$ but $C \subseteq E$.Would the correct form of the second requirement be that:For each $(u, v) \in E - C$ there exists an edge in $C$ that is adjacent to either $u$ or $v$?
Is there a typo in this definition of Minimal Maximal Matching
graph theory;matching
I gave a quick look, it looks like you didn't copy the definition right, the second requirement state that if $u$ e $v$ belong to $D$, not $C$, then $(u,v) \notin E$, where $D = \bigcup_{e \in C}e$. What I guess they mean is that if, say, $(a,b)$ and $(c,d)$ belong to $C$ and $(u,a)$, $(c,v)$ belong to $E$ then $(u,v) \notin E$ otherwise it could be added to $C$ and it would still be a valid matching.